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MARC Lista (tabellare)
Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations [[electronic resource] ] : VIASM 2016 / / by Nam Q. Le, Hiroyoshi Mitake, Hung V. Tran ; edited by Hiroyoshi Mitake, Hung V. Tran
Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations [[electronic resource] ] : VIASM 2016 / / by Nam Q. Le, Hiroyoshi Mitake, Hung V. Tran ; edited by Hiroyoshi Mitake, Hung V. Tran
Autore Le Nam Q
Edizione [1st ed. 2017.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
Descrizione fisica 1 online resource (VII, 228 p. 16 illus., 1 illus. in color.)
Disciplina 515.353
Collana Lecture Notes in Mathematics
Soggetto topico Partial differential equations
Calculus of variations
Differential geometry
Partial Differential Equations
Calculus of Variations and Optimal Control; Optimization
Differential Geometry
ISBN 3-319-54208-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- Part I The Second Boundary Value Problem of the Prescribed Affine Mean Curvature Equation and Related Linearized Monge-Ampère Equation -- Introduction -- Notation -- 1 The Affine Bernstein and Boundary Value Problems -- 1.1 The Affine Bernstein and Boundary Value Problems -- 1.1.1 Minimal Graph -- 1.1.2 Affine Maximal Graph -- 1.1.3 The Affine Bernstein Problem -- 1.1.4 Connection with the Constant Scalar Curvature Problem -- 1.1.5 The First Boundary Value Problem -- 1.1.6 The Second Boundary Value Problem of the Prescribed Affine Mean Curvature Equation -- 1.1.7 Solvability of the Second Boundary Value Problem -- 1.2 Existence of Solution to the Second Boundary Value Problem -- 1.2.1 Existence of Solution via Degree Theory and A Priori Estimates -- 1.2.2 Several Boundary Regularity Results for Monge-Ampère and Linearized Monge-Ampère Equations -- 1.3 Proof of Global W4,p and C4,α Estimates -- 1.3.1 Test Functions -- 1.3.2 L1 Bound and Lower Bound on the Hessian Determinant -- 1.3.3 Gradient Bound -- 1.3.4 Legendre Transform and Upper Bound on Hessian Determinant -- References -- 2 The Linearized Monge-Ampère Equation -- 2.1 The Linearized Monge-Ampère Equation and Interior Regularity of Its Solution -- 2.1.1 The Linearized Monge-Ampère Equation -- 2.1.2 Linearized Monge-Ampère Equations in Contexts -- 2.1.3 Difficulties and Expected Regularity -- 2.1.4 Affine Invariance Property -- 2.1.5 Krylov-Safonov's Harnack Inequality -- 2.1.6 Harnack Inequality for the Linearized Monge-Ampère Equation -- 2.2 Interior Harnack and Hölder Estimates for Linearized Monge-Ampère -- 2.2.1 Proof of Caffarelli-Gutiérrez's Harnack Inequality -- 2.2.2 Proof of the Interior Hölder Estimates for the Inhomogeneous Linearized Monge-Ampère Equation -- 2.3 Global Hölder Estimates for the Linearized Monge-Ampère Equations.
2.3.1 Boundary Hölder Continuity for Solutions of Non-uniformly Elliptic Equations -- 2.3.2 Savin's Localization Theorem -- 2.3.3 Proof of Global Hölder Estimates for the Linearized Monge-Ampère Equation -- References -- 3 The Monge-Ampère Equation -- 3.1 Maximum Principles and Sections of the Monge-Ampère Equation -- 3.1.1 Basic Definitions -- 3.1.2 Examples and Properties of the Normal Mapping and the Monge-Ampère Measure -- 3.1.3 Maximum Principles -- 3.1.4 John's Lemma -- 3.1.5 Comparison Principle and Applications -- 3.1.6 The Dirichlet Problem and Perron's Method -- 3.1.7 Sections of Convex Functions -- 3.2 Geometry of Sections of Solutions to the Monge-Ampère Equation -- 3.2.1 Compactness of Solutions to the Monge-Ampère Equation -- 3.2.2 Caffarelli's Localization Theorem -- 3.2.3 Strict Convexity and C1,α Estimates -- 3.2.4 Engulfing Property of Sections -- Appendix A: Auxiliary Lemmas -- Appendix B: A Heuristic Explanation of Trudinger-Wang's Non-smooth Example -- References -- Part II Dynamical Properties of Hamilton-Jacobi Equations via the Nonlinear Adjoint Method: Large Time Behavior and Discounted Approximation -- Introduction -- Notations -- References -- 4 Ergodic Problems for Hamilton-Jacobi Equations -- 4.1 Motivation -- 4.2 Existence of Solutions to Ergodic Problems -- References -- 5 Large Time Asymptotics of Hamilton-Jacobi Equations -- 5.1 A Brief Introduction -- 5.2 First-Order Case with Separable Hamiltonians -- 5.2.1 First Example -- 5.2.2 Second Example -- 5.3 First-Order Case with General Hamiltonians -- 5.3.1 Formal Calculation -- 5.3.2 Regularizing Process -- 5.3.3 Conservation of Energy and a Key Observation -- 5.3.4 Proof of Key Estimates -- 5.4 Degenerate Viscous Case -- 5.5 Asymptotic Profile of the First-Order Case -- 5.6 Viscous Case -- 5.7 Some Other Directions and Open Questions -- References.
6 Selection Problems in the Discounted Approximation Procedure -- 6.1 Selection Problems -- 6.1.1 Examples on Nonuniqueness of Ergodic Problems -- 6.1.2 Discounted Approximation -- 6.2 Regularizing Process -- 6.2.1 Regularizing Process and Construction of M -- 6.2.2 Stochastic Mather Measures -- 6.2.3 Key Estimates -- 6.3 Proof of Theorem 6.5 -- 6.4 Proof of the Commutation Lemma -- 6.5 Applications -- 6.5.1 Limit of u in Example 6.1 -- 6.5.2 Limit of u in Examples 6.3, 6.4 -- 6.6 Some Other Directions and Open Questions -- 6.6.1 Discounted Approximation Procedure -- 6.6.2 Vanishing Viscosity Procedure -- 6.6.3 Selection of Mather Measures -- References -- 7 Appendix of Part II -- 7.1 Motivation and Examples -- 7.1.1 Front Propagation Problems -- 7.1.2 Optimal Control Problems -- 7.1.2.1 Inviscid Cases -- 7.1.2.2 Viscous Cases -- 7.2 Definitions -- 7.3 Consistency -- 7.4 Comparison Principle and Uniqueness -- 7.5 Stability -- 7.6 Lipschitz Estimates -- 7.7 The Perron Method -- References.
Record Nr. UNISA-996466643603316
Le Nam Q  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations [[electronic resource] ] : VIASM 2016 / / by Nam Q. Le, Hiroyoshi Mitake, Hung V. Tran ; edited by Hiroyoshi Mitake, Hung V. Tran
Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations [[electronic resource] ] : VIASM 2016 / / by Nam Q. Le, Hiroyoshi Mitake, Hung V. Tran ; edited by Hiroyoshi Mitake, Hung V. Tran
Autore Le Nam Q
Edizione [1st ed. 2017.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
Descrizione fisica 1 online resource (VII, 228 p. 16 illus., 1 illus. in color.)
Disciplina 515.353
Collana Lecture Notes in Mathematics
Soggetto topico Partial differential equations
Calculus of variations
Differential geometry
Partial Differential Equations
Calculus of Variations and Optimal Control; Optimization
Differential Geometry
ISBN 3-319-54208-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- Part I The Second Boundary Value Problem of the Prescribed Affine Mean Curvature Equation and Related Linearized Monge-Ampère Equation -- Introduction -- Notation -- 1 The Affine Bernstein and Boundary Value Problems -- 1.1 The Affine Bernstein and Boundary Value Problems -- 1.1.1 Minimal Graph -- 1.1.2 Affine Maximal Graph -- 1.1.3 The Affine Bernstein Problem -- 1.1.4 Connection with the Constant Scalar Curvature Problem -- 1.1.5 The First Boundary Value Problem -- 1.1.6 The Second Boundary Value Problem of the Prescribed Affine Mean Curvature Equation -- 1.1.7 Solvability of the Second Boundary Value Problem -- 1.2 Existence of Solution to the Second Boundary Value Problem -- 1.2.1 Existence of Solution via Degree Theory and A Priori Estimates -- 1.2.2 Several Boundary Regularity Results for Monge-Ampère and Linearized Monge-Ampère Equations -- 1.3 Proof of Global W4,p and C4,α Estimates -- 1.3.1 Test Functions -- 1.3.2 L1 Bound and Lower Bound on the Hessian Determinant -- 1.3.3 Gradient Bound -- 1.3.4 Legendre Transform and Upper Bound on Hessian Determinant -- References -- 2 The Linearized Monge-Ampère Equation -- 2.1 The Linearized Monge-Ampère Equation and Interior Regularity of Its Solution -- 2.1.1 The Linearized Monge-Ampère Equation -- 2.1.2 Linearized Monge-Ampère Equations in Contexts -- 2.1.3 Difficulties and Expected Regularity -- 2.1.4 Affine Invariance Property -- 2.1.5 Krylov-Safonov's Harnack Inequality -- 2.1.6 Harnack Inequality for the Linearized Monge-Ampère Equation -- 2.2 Interior Harnack and Hölder Estimates for Linearized Monge-Ampère -- 2.2.1 Proof of Caffarelli-Gutiérrez's Harnack Inequality -- 2.2.2 Proof of the Interior Hölder Estimates for the Inhomogeneous Linearized Monge-Ampère Equation -- 2.3 Global Hölder Estimates for the Linearized Monge-Ampère Equations.
2.3.1 Boundary Hölder Continuity for Solutions of Non-uniformly Elliptic Equations -- 2.3.2 Savin's Localization Theorem -- 2.3.3 Proof of Global Hölder Estimates for the Linearized Monge-Ampère Equation -- References -- 3 The Monge-Ampère Equation -- 3.1 Maximum Principles and Sections of the Monge-Ampère Equation -- 3.1.1 Basic Definitions -- 3.1.2 Examples and Properties of the Normal Mapping and the Monge-Ampère Measure -- 3.1.3 Maximum Principles -- 3.1.4 John's Lemma -- 3.1.5 Comparison Principle and Applications -- 3.1.6 The Dirichlet Problem and Perron's Method -- 3.1.7 Sections of Convex Functions -- 3.2 Geometry of Sections of Solutions to the Monge-Ampère Equation -- 3.2.1 Compactness of Solutions to the Monge-Ampère Equation -- 3.2.2 Caffarelli's Localization Theorem -- 3.2.3 Strict Convexity and C1,α Estimates -- 3.2.4 Engulfing Property of Sections -- Appendix A: Auxiliary Lemmas -- Appendix B: A Heuristic Explanation of Trudinger-Wang's Non-smooth Example -- References -- Part II Dynamical Properties of Hamilton-Jacobi Equations via the Nonlinear Adjoint Method: Large Time Behavior and Discounted Approximation -- Introduction -- Notations -- References -- 4 Ergodic Problems for Hamilton-Jacobi Equations -- 4.1 Motivation -- 4.2 Existence of Solutions to Ergodic Problems -- References -- 5 Large Time Asymptotics of Hamilton-Jacobi Equations -- 5.1 A Brief Introduction -- 5.2 First-Order Case with Separable Hamiltonians -- 5.2.1 First Example -- 5.2.2 Second Example -- 5.3 First-Order Case with General Hamiltonians -- 5.3.1 Formal Calculation -- 5.3.2 Regularizing Process -- 5.3.3 Conservation of Energy and a Key Observation -- 5.3.4 Proof of Key Estimates -- 5.4 Degenerate Viscous Case -- 5.5 Asymptotic Profile of the First-Order Case -- 5.6 Viscous Case -- 5.7 Some Other Directions and Open Questions -- References.
6 Selection Problems in the Discounted Approximation Procedure -- 6.1 Selection Problems -- 6.1.1 Examples on Nonuniqueness of Ergodic Problems -- 6.1.2 Discounted Approximation -- 6.2 Regularizing Process -- 6.2.1 Regularizing Process and Construction of M -- 6.2.2 Stochastic Mather Measures -- 6.2.3 Key Estimates -- 6.3 Proof of Theorem 6.5 -- 6.4 Proof of the Commutation Lemma -- 6.5 Applications -- 6.5.1 Limit of u in Example 6.1 -- 6.5.2 Limit of u in Examples 6.3, 6.4 -- 6.6 Some Other Directions and Open Questions -- 6.6.1 Discounted Approximation Procedure -- 6.6.2 Vanishing Viscosity Procedure -- 6.6.3 Selection of Mather Measures -- References -- 7 Appendix of Part II -- 7.1 Motivation and Examples -- 7.1.1 Front Propagation Problems -- 7.1.2 Optimal Control Problems -- 7.1.2.1 Inviscid Cases -- 7.1.2.2 Viscous Cases -- 7.2 Definitions -- 7.3 Consistency -- 7.4 Comparison Principle and Uniqueness -- 7.5 Stability -- 7.6 Lipschitz Estimates -- 7.7 The Perron Method -- References.
Record Nr. UNINA-9910257380003321
Le Nam Q  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Einstein’s Field Equations and Their Physical Implications [[electronic resource] ] : Selected Essays in Honour of Jürgen Ehlers / / edited by Bernd G. Schmidt
Einstein’s Field Equations and Their Physical Implications [[electronic resource] ] : Selected Essays in Honour of Jürgen Ehlers / / edited by Bernd G. Schmidt
Edizione [1st ed. 2000.]
Pubbl/distr/stampa Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2000
Descrizione fisica 1 online resource (XIII, 433 p.)
Disciplina 530.11
Collana Lecture Notes in Physics
Soggetto topico Differential geometry
Gravitation
Physics
Differential Geometry
Classical and Quantum Gravitation, Relativity Theory
Mathematical Methods in Physics
ISBN 3-540-46580-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Selected Solutions of Einstein’s Field Equations: Their Role in General Relativity and Astrophysics -- The Cauchy Problem for the Einstein Equations -- Post-Newtonian Gravitational Radiation -- Duality and Hidden Symmetries in Gravitational Theories -- Time-Independent Gravitational Fields -- Gravitational Lensing from a Geometric Viewpoint.
Record Nr. UNINA-9910139813603321
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2000
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Einstein’s Field Equations and Their Physical Implications [[electronic resource] ] : Selected Essays in Honour of Jürgen Ehlers / / edited by Bernd G. Schmidt
Einstein’s Field Equations and Their Physical Implications [[electronic resource] ] : Selected Essays in Honour of Jürgen Ehlers / / edited by Bernd G. Schmidt
Edizione [1st ed. 2000.]
Pubbl/distr/stampa Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2000
Descrizione fisica 1 online resource (XIII, 433 p.)
Disciplina 530.11
Collana Lecture Notes in Physics
Soggetto topico Differential geometry
Gravitation
Physics
Differential Geometry
Classical and Quantum Gravitation, Relativity Theory
Mathematical Methods in Physics
ISBN 3-540-46580-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Selected Solutions of Einstein’s Field Equations: Their Role in General Relativity and Astrophysics -- The Cauchy Problem for the Einstein Equations -- Post-Newtonian Gravitational Radiation -- Duality and Hidden Symmetries in Gravitational Theories -- Time-Independent Gravitational Fields -- Gravitational Lensing from a Geometric Viewpoint.
Record Nr. UNISA-996466685503316
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2000
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Elementary Symplectic Topology and Mechanics [[electronic resource] /] / by Franco Cardin
Elementary Symplectic Topology and Mechanics [[electronic resource] /] / by Franco Cardin
Autore Cardin Franco
Edizione [1st ed. 2015.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
Descrizione fisica 1 online resource (237 p.)
Disciplina 510
515.64
516.36
530.15
Collana Lecture Notes of the Unione Matematica Italiana
Soggetto topico Mathematical physics
Differential geometry
Calculus of variations
Mathematical Physics
Differential Geometry
Calculus of Variations and Optimal Control; Optimization
ISBN 3-319-11026-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Beginning -- Notes on Differential Geometry -- Symplectic Manifolds -- Poisson brackets environment -- Cauchy Problem for H-J equations -- Calculus of Variations and Conjugate Points -- Asymptotic Theory of Oscillating Integrals -- Lusternik-Schnirelman and Morse -- Finite Exact Reductions -- Other instances -- Bibliography.
Record Nr. UNINA-9910299778503321
Cardin Franco  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Elements of General Relativity [[electronic resource] /] / by Piotr T. Chruściel
Elements of General Relativity [[electronic resource] /] / by Piotr T. Chruściel
Autore Chruściel Piotr T
Edizione [1st ed. 2019.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2019
Descrizione fisica 1 online resource (IX, 283 p. 53 illus., 46 illus. in color.)
Disciplina 530.11
Collana Compact Textbooks in Mathematics
Soggetto topico Differential geometry
Gravitation
Differential Geometry
Classical and Quantum Gravitation, Relativity Theory
ISBN 3-030-28416-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Introduction to tensor calculus and Riemannian geometry -- Curved space-time -- The Schwarzschild metric -- Weak fields, gravitational waves -- Stars -- Cosmology.
Record Nr. UNINA-9910383831003321
Chruściel Piotr T  
Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2019
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Encyclopedia of Distances [[electronic resource] /] / by Michel Marie Deza, Elena Deza
Encyclopedia of Distances [[electronic resource] /] / by Michel Marie Deza, Elena Deza
Autore Deza Michel Marie
Edizione [4th ed. 2016.]
Pubbl/distr/stampa Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2016
Descrizione fisica 1 online resource (XXII, 756 p. 2 illus.)
Disciplina 516.36
Soggetto topico Differential geometry
Topology
Computer mathematics
Applied mathematics
Engineering mathematics
Differential Geometry
Computational Mathematics and Numerical Analysis
Mathematical and Computational Engineering
ISBN 3-662-52844-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Part I. Mathematics of Distances: 1 General Definitions -- 2 Topological Spaces -- 3 Generalization of Metric Spaces -- 4 Metric Transforms -- 5 Metrics on Normed Structures -- Part II. Geometry and Distances: 6 Distances in Geometry -- 7 Riemannian and Hermitian Metrics -- 8 Distances on Surfaces and Knots -- 9 Distances on Convex Bodies, Cones and Simplicial Complexes -- Part III. Distances in Classical Mathematics: 10 Distances in Algebra -- 11 Distances on Strings and Permutations -- 12 Distances on Numbers, Polynomials and Matrices -- 13 Distances in Functional Analysis -- 14 Distances in Probability Theory -- Part IV. Distances in Applied Mathematics: 15 Distances in Graph Theory -- 16 Distances in Coding Theory -- 17 Distances and Similarities in Data Analysis -- 18 Distances in Systems and Mathematical Engineering -- Part V. Computer-Related Distances: 19 Distances on Real and Digital Planes -- 20 Voronoi Diagram Distances -- 21 Image and Audio Distances -- 22 Distances in Networks -- Part VI. Distances in Natural Sciences: 23 Distances in Biology -- 24 Distances in Physics and Chemistry -- 25 Distances in Earth Science and Astronomy -- 26 Distances in Cosmology and Theory of Relativity -- Part VII. Real-World Distances: 27 Length Measures and Scales -- 28 Distances in Applied Social Sciences -- 29 Other Distances.
Record Nr. UNINA-9910254083903321
Deza Michel Marie  
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2016
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Encyclopedia of Distances [[electronic resource] /] / by Michel Marie Deza, Elena Deza
Encyclopedia of Distances [[electronic resource] /] / by Michel Marie Deza, Elena Deza
Autore Deza Michel Marie
Edizione [3rd ed. 2014.]
Pubbl/distr/stampa Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2014
Descrizione fisica 1 online resource (731 p.)
Disciplina 004
510
514
516
Soggetto topico Geometry
Differential geometry
Topology
Computer mathematics
Mathematics
Visualization
Applied mathematics
Engineering mathematics
Differential Geometry
Computational Mathematics and Numerical Analysis
Mathematical and Computational Engineering
ISBN 3-662-44342-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Part I. Mathematics of Distances: 1 General Definitions -- 2 Topological Spaces -- 3 Generalization of Metric Spaces -- 4 Metric Transforms -- 5 Metrics on Normed Structures -- Part II. Geometry and Distances: 6 Distances in Geometry -- 7 Riemannian and Hermitian Metrics -- 8 Distances on Surfaces and Knots -- 9 Distances on Convex Bodies, Cones and Simplicial Complexes -- Part III. Distances in Classical Mathematics: 10 Distances in Algebra -- 11 Distances on Strings and Permutations -- 12 Distances on Numbers, Polynomials and Matrices -- 13 Distances in Functional Analysis -- 14 Distances in Probability Theory -- Part IV. Distances in Applied Mathematics: 15 Distances in Graph Theory -- 16 Distances in Coding Theory -- 17 Distances and Similarities in Data Analysis -- 18 Distances in Systems and Mathematical Engineering -- Part V. Computer-Related Distances: 19 Distances on Real and Digital Planes -- 20 Voronoi Diagram Distances -- 21 Image and Audio Distances -- 22 Distances in Networks -- Part VI. Distances in Natural Sciences: 23 Distances in Biology -- 24 Distances in Physics and Chemistry -- 25 Distances in Earth Science and Astronomy -- 26 Distances in Cosmology and Theory of Relativity -- Part VII. Real-World Distances: 27 Length Measures and Scales -- 28 Distances in Applied Social Sciences -- 29 Other Distances.
Record Nr. UNINA-9910299980903321
Deza Michel Marie  
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2014
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees [[electronic resource] ] : Applications to Non-Archimedean Diophantine Approximation / / by Anne Broise-Alamichel, Jouni Parkkonen, Frédéric Paulin
Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees [[electronic resource] ] : Applications to Non-Archimedean Diophantine Approximation / / by Anne Broise-Alamichel, Jouni Parkkonen, Frédéric Paulin
Autore Broise-Alamichel Anne
Edizione [1st ed. 2019.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2019
Descrizione fisica 1 online resource (viii, 413 pages) : illustrations
Disciplina 516.362
Collana Progress in Mathematics
Soggetto topico Dynamics
Ergodic theory
Differential geometry
Group theory
Number theory
Convex geometry 
Discrete geometry
Probabilities
Dynamical Systems and Ergodic Theory
Differential Geometry
Group Theory and Generalizations
Number Theory
Convex and Discrete Geometry
Probability Theory and Stochastic Processes
ISBN 3-030-18315-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Introduction -- Negatively curved geometry -- Potentials, critical exponents and Gibbs cocycles -- Patterson-Sullivan and Bowen-Margulis measures with potential on CAT(-1) spaces -- Symbolic dynamics of geodesic flows on trees -- Random walks on weighted graphs of groups -- Skinning measures with potential on CAT(-1) spaces -- Explicit measure computations for simplicial trees and graphs of groups -- Rate of mixing for the geodesic flow -- Equidistribution of equidistant level sets to Gibbs measures -- Equidistribution of common perpendicular arcs -- Equidistribution and counting of common perpendiculars in quotient spaces -- Geometric applications -- Fields with discrete valuations -- Bruhat-Tits trees and modular groups -- Rational point equidistribution and counting in completed function fields -- Equidistribution and counting of quadratic irrational points in non-Archimedean local fields -- Counting and equidistribution of crossratios -- Counting and equidistribution of integral representations by quadratic norm forms -- A - A weak Gibbs measure is the unique equilibrium, by J. Buzzi -- List of Symbols -- Index -- Bibliography.
Record Nr. UNINA-9910364957603321
Broise-Alamichel Anne  
Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2019
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Ergodic Theory and Negative Curvature [[electronic resource] ] : CIRM Jean-Morlet Chair, Fall 2013 / / edited by Boris Hasselblatt
Ergodic Theory and Negative Curvature [[electronic resource] ] : CIRM Jean-Morlet Chair, Fall 2013 / / edited by Boris Hasselblatt
Edizione [1st ed. 2017.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
Descrizione fisica 1 online resource (VII, 328 p. 68 illus., 17 illus. in color.)
Disciplina 515.352
Collana Lecture Notes in Mathematics
Soggetto topico Dynamics
Ergodic theory
Differential geometry
Dynamical Systems and Ergodic Theory
Differential Geometry
ISBN 3-319-43059-9
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- 1 Introduction to Hyperbolic Dynamics and Ergodic Theory -- 1.1 Introduction -- 1.1.1 Guided Tour -- 1.1.2 Examples -- 1.1.3 Hyperbolic Dynamics -- 1.2 Historical Sketch -- 1.2.1 Homoclinic Tangles -- 1.2.2 Geodesic Flows -- 1.2.3 Boltzmann's Fundamental Postulate -- 1.2.4 Picking Up from Poincaré -- 1.2.5 Modern Hyperbolic Dynamics -- 1.3 Hyperbolic Sets: Shadowing and Expansiveness -- 1.3.1 Definitions -- 1.3.2 Invariant Cones -- 1.3.3 Shadowing, Expansiveness, Closing -- 1.3.4 Specification -- 1.3.5 Spectral Decomposition -- 1.3.6 Stability -- 1.4 The Shadowing Theorem: Stability, Symbolic Models -- 1.4.1 The Shadowing Theorem -- 1.4.2 Stability -- 1.4.3 Markov Models -- 1.5 Basic Ergodic Theory of Hyperbolic Sets -- 1.5.1 Ergodicity and Related Notions -- 1.5.2 The Hopf Argument -- 1.5.3 Mixing from the Hopf Argument -- 1.5.4 Multiple Mixing from the One-Sided Hopf Argument -- 1.6 Contractions and Invariant Manifolds -- 1.6.1 The Contraction-Mapping Principle -- 1.6.2 The Spectrum of a Linear Map -- 1.6.3 Hyperbolic Linear Maps -- 1.6.4 Stable and Unstable Manifolds of a Fixed Point -- 1.6.5 Stable and Unstable Foliations -- 1.6.6 Applications: Livschitz Theory and Local Product Structure -- 1.6.6.1 Exponential Closing -- 1.6.6.2 The Livschitz Theorem -- 1.6.6.3 Smooth Invariant Measures for Anosov Diffeomorphisms -- 1.6.6.4 Local Product Structure -- 1.7 Ergodic Theory -- 1.7.1 Asymptotic Distribution, Invariant Measures -- 1.7.2 Existence of Invariant Measures and Recurrence -- 1.7.3 The Birkhoff Ergodic Theorem -- 1.7.4 Existence of Asymptotic Distribution -- 1.7.5 The Birkhoff Ergodic Theorem for Flows -- 1.7.6 The von Neumann Mean Ergodic Theorem -- 1.7.7 Ergodicity and Unique Ergodicity -- 1.7.8 Isomorphism and Factors -- 1.7.9 Topological and Probabilistic Recurrence -- 1.7.10 Ergodicity of Translations.
1.7.10.1 First Proof of Unique Ergodicity -- 1.7.10.2 Second Proof of Unique Ergodicity -- 1.7.10.3 A Third Proof and an Application -- 1.7.11 Circle Homeomorphisms -- 1.7.12 Extensions of Rotations -- 1.7.13 Ergodicity of Expanding Maps and Toral Automorphisms -- 1.7.14 The Gauss Map -- 1.7.15 Bernoulli Shifts -- 1.7.16 Mixing -- 1.7.17 Toral Translations and Expanding Maps -- 1.7.18 Rates of Mixing and Decay of Correlations -- 1.7.19 Spectral Isomorphism and Invariants -- References -- 2 On Iteration and Asymptotic Solutions of Differential Equations by Jacques Hadamard -- 3 Dynamics of Geodesic and Horocyclic Flows -- 3.1 Introduction -- 3.1.1 First Exercises -- 3.2 Topological Dynamics of the Horocyclic Flow -- 3.2.1 Nonarithmeticity, Mixing of the Geodesic Flow, Density of Horocycles -- 3.2.2 The Horocycle (hsv) Is Dense Iff the Geodesic (gt v) Is Not Quasiminimizing -- 3.2.3 Geometrically Finite Surfaces -- 3.2.4 Some More Exercises -- 3.3 Invariant Measures for the Horocyclic Flow -- 3.3.1 The Hopf Coordinates -- 3.3.2 The Hopf Argument, Ergodicity and Mixing of the Liouville Measure -- 3.3.3 Unique Ergodicity of the Horocyclic Flow -- 3.3.4 The Finite Volume Case -- 3.3.4.1 About the Proof of Unique Ergodicity -- 3.3.4.2 Nondivergence of Horocycles -- 3.3.4.3 Conclusion of the Proof -- 3.3.5 Geometrically Finite Case -- 3.3.5.1 The Patterson-Sullivan Construction -- 3.3.5.2 The Burger-Roblin Measure -- 3.3.5.3 Equidistribution of Horocycles Towards the Bowen-Margulis Measure -- 3.3.6 Geometrically Infinite Surfaces -- 3.3.7 Exercises -- References -- 4 Ergodicity of the Weil-Petersson Geodesic Flow -- 4.1 The Proof of Ergodicity -- 4.1.1 The Ergodicity Theorem -- 4.1.2 Hyperbolic Dynamics -- 4.1.3 The Hopf Argument -- 4.1.4 Nonuniform Hyperbolicity -- 4.1.5 Addressing Singularities: The Katok-Strelcyn Criteria.
4.1.6 The Case of the Punctured Torus -- 4.2 Geodesic Flows -- 4.2.1 Vertical and Horizontal Subspaces and the Sasaki Metric -- 4.2.2 The Geodesic Flow and Jacobi Fields -- 4.2.3 Matrix Jacobi and Riccati Equations -- 4.2.4 Perpendicular Jacobi Fields and Invariant Subbundles -- 4.2.5 Consequences of Negative Curvature and Unstable Jacobi Fields -- 4.3 An Ergodicity Criterion for Incomplete Geodesic Flows -- References -- 5 Ergodicity of Geodesic Flows on Incomplete Negatively Curved Manifolds -- 5.1 Introduction -- 5.1.1 Ergodicity Criterion for a Certain Class of Geodesic Flows -- 5.1.2 Outline of Proof of Theorem 5.1.1 -- 5.1.2.1 Hopf's Argument for Anosov Systems -- 5.1.2.2 Hopf's Argument in the Context of Singular Hyperbolic Geodesic Flows -- 5.1.3 Organization of the Text -- 5.2 Geometry of Tangent Bundles -- 5.2.1 Riemannian Metrics and Curvature Tensors -- 5.2.2 The Tangent Bundle to a Tangent Bundle -- 5.3 First Derivative of Geodesic Flows and Jacobi Fields -- 5.3.1 Computation of the First Derivative of Geodesic Flows -- 5.3.2 Perpendicular Jacobi Fields and Invariant Subbundles -- 5.3.3 Matrix Jacobi and Ricatti Equations -- 5.3.4 An Estimate for the First Derivative of a Geodesic Flow -- 5.4 Hyperbolicity of Certain Geodesic Flows -- 5.5 Stable Manifolds of Certain Geodesic Flows -- 5.5.1 Local (Pesin) Stable Manifolds for Certain Geodesic Flows -- 5.5.2 Global Stable Manifolds of Certain Geodesic Flows -- 5.5.2.1 Stable Jacobi Fields and Stable Horospheres -- 5.5.2.2 Geometry of the Stable and Unstable Horospheres -- 5.5.2.3 Absolute Continuity of Global Stable Manifolds -- 5.6 Proof of Theorem 5.1.1 via Hopf's Argument -- References -- 6 The Dynamics of the Weil-Petersson Flow -- 6.1 Introduction -- 6.1.1 An Overview of the Dynamics of WP Flow -- 6.1.2 Ergodicity of WP Flow: Outline of Proof.
6.1.2.1 A Quick Review of Hopf's Argument -- 6.1.2.2 Hopf's Argument in the Context of WP Flow -- 6.1.2.3 A Brief Comment on the Verification of the Ergodicity Criterion for WP Flow -- 6.1.3 Rates of Mixing of WP Flow -- 6.1.4 Organization of the Text -- 6.2 Moduli Spaces of Riemann Surfaces and the Weil-Petersson Metric -- 6.2.1 Definition and Examples of Moduli Spaces -- 6.2.2 Teichmüller Metric -- 6.2.3 Teichmüller Spaces and Mapping-Class Groups -- 6.2.4 Fenchel-Nielsen Coordinates -- 6.2.5 Cotangent Bundle to Moduli Spaces of Riemann Surfaces -- 6.2.6 Integrable Quadratic Differentials -- 6.2.7 Teichmüller and Weil-Petersson Metrics -- 6.2.8 Ergodicity of WP Flow: Outline of Proof Revisited -- 6.3 Geometry of the Weil-Petersson Metric -- 6.3.1 Items (I) and (II) of Theorem 3 for WP Metric -- 6.3.2 Item (III) of Theorem 3 for WP Metric -- 6.3.3 Item (IV) of Theorem 3 for WP Metric -- 6.3.3.1 Wolpert's Formulas for the Curvatures of the WP Metric -- 6.3.3.2 Bounds for the First Two Derivatives of WP Metric: Overview -- 6.3.3.3 Quasi-Fuchsian Locus QF(S) and McMullen's 1-Forms θWP -- 6.3.3.4 ``Cauchy Estimate'' of ωWP After Burns-Masur-Wilkinson -- 6.3.4 Item (V) of Theorem 3 for WP Metric -- 6.3.5 Item (VI) of Theorem 3 for WP Flow -- 6.4 Decay of Correlations for the Weil-Petersson Geodesic Flow -- 6.4.1 Rates of Mixing of the WP Flow on T1Mg,n I: Proof of Theorem 11 -- 6.4.2 Rates of Mixing of the WP Flow on T1Mg,n II: Proof of Theorem 12 -- 6.4.2.1 Excursions Near the Cusp and Suspension Flows -- 6.4.2.2 Rapid Mixing of Contact Suspension Flows -- 6.4.2.3 The Derivative of the Roof Function -- 6.4.2.4 Some Estimates for the Expansion Factors Λ(β) -- References -- 7 A Survey of Some Arithmetic Applications of Ergodic Theory in Negative Curvature -- 7.1 Introduction -- 7.2 Arithmetic Applications.
7.2.1 Basic and Classic Diophantine Approximation -- 7.2.2 An Approximation Framework -- 7.2.3 Diophantine Approximation in R by Quadratic Irrationals -- 7.2.4 Equidistribution of Rational Points in R and C -- 7.2.5 Equidistribution and Counting in the Heisenberg Group -- 7.3 Measures in Negative Curvature -- 7.3.1 A Classical Link Between Basic Diophantine Approximation and Hyperbolic Geometry -- 7.3.2 Negative Curvature Background -- 7.3.3 The Various Measures -- 7.4 Geometric Equidistribution and Counting -- 7.4.1 Equidistribution and Counting of Common Perpendicular -- 7.4.2 Towards the Arithmetic Applications -- References.
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
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