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Circle-valued Morse theory [[electronic resource] /] / Andrei V. Pajitnov
| Circle-valued Morse theory [[electronic resource] /] / Andrei V. Pajitnov |
| Autore | Pajitnov Andrei V |
| Pubbl/distr/stampa | Berlin ; ; New York, : De Gruyter, c2006 |
| Descrizione fisica | 1 online resource (464 pages) |
| Disciplina | 514/.74 |
| Collana | De Gruyter studies in mathematics |
| Soggetto topico |
Morse theory
Manifolds (Mathematics) |
| Soggetto non controllato |
Differential geometry
Morse theory |
| ISBN |
1-282-19426-7
9786612194269 3-11-019797-9 |
| Classificazione | SK 350 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Preface -- Introduction -- Part 1. Morse functions and vector fields on manifolds -- CHAPTER 1. Vector fields and C0 topology -- CHAPTER 2. Morse functions and their gradients -- CHAPTER 3. Gradient flows of real-valued Morse functions -- Part 2. Transversality, handles, Morse complexes -- CHAPTER 4. The Kupka-Smale transversality theory for gradient flows -- CHAPTER 5. Handles -- CHAPTER 6. The Morse complex of a Morse function -- Part 3. Cellular gradients -- CHAPTER 7. Condition (C) -- CHAPTER 8. Cellular gradients are C0-generic -- CHAPTER 9. Properties of cellular gradients -- Part 4. Circle-valued Morse maps and Novikov complexes -- CHAPTER 10. Completions of rings, modules and complexes -- CHAPTER 11. The Novikov complex of a circle-valued Morse map -- CHAPTER 12. Cellular gradients of circle-valued Morse functions and the Rationality Theorem -- CHAPTER 13. Counting closed orbits of the gradient flow -- CHAPTER 14. Selected topics in the Morse-Novikov theory -- Backmatter |
| Record Nr. | UNINA-9910782523503321 |
Pajitnov Andrei V
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| Berlin ; ; New York, : De Gruyter, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Elementary Symplectic Topology and Mechanics / Franco Cardin
| Elementary Symplectic Topology and Mechanics / Franco Cardin |
| Autore | Cardin, Franco |
| Pubbl/distr/stampa | Cham, : Springer, : Unione Matematica Italiana, 2015 |
| Descrizione fisica | xvii, 222 p. : ill. ; 24 cm |
| Soggetto topico |
53Dxx - Symplectic geometry, contact geometry [MSC 2020]
37Jxx - Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems [MSC 2020] 58Exx - Variational problems in infinite-dimensional spaces [MSC 2020] 53Zxx - Applications of differential geometry to sciences and engineering [MSC 2020] 35F21 - Hamilton-Jacobi equations [MSC 2020] |
| Soggetto non controllato |
Hamilton-Jacobi Equation
Lusternik-Schnirelman theory Morse theory Symplectic geometry Viterbo symplectic topology |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN0125308 |
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Cardin, Franco
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| Cham, : Springer, : Unione Matematica Italiana, 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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Elementary Symplectic Topology and Mechanics / Franco Cardin
| Elementary Symplectic Topology and Mechanics / Franco Cardin |
| Autore | Cardin, Franco |
| Pubbl/distr/stampa | Cham, : Springer, : Unione Matematica Italiana, 2015 |
| Descrizione fisica | xvii, 222 p. : ill. ; 24 cm |
| Soggetto topico |
35F21 - Hamilton-Jacobi equations [MSC 2020]
37Jxx - Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems [MSC 2020] 53Dxx - Symplectic geometry, contact geometry [MSC 2020] 53Zxx - Applications of differential geometry to sciences and engineering [MSC 2020] 58Exx - Variational problems in infinite-dimensional spaces [MSC 2020] |
| Soggetto non controllato |
Hamilton-Jacobi Equation
Lusternik-Schnirelman theory Morse theory Symplectic geometry Viterbo symplectic topology |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other physical topics. A central feature is the systematic utilization of Lagrangian submanifolds and their Maslov-Hörmander generating functions. Following this line of thought, first introduced by Wlodemierz Tulczyjew, geometric solutions of Hamilton-Jacobi equations, Hamiltonian vector fields and canonical transformations are described by suitable Lagrangian submanifolds belonging to distinct well-defined symplectic structures. This unified point of view has been particularly fruitful in symplectic topology, which is the modern Hamiltonian environment for the calculus of variations, yielding sharp sufficient existence conditions. This line of investigation was initiated by Claude Viterbo in 1992; here, some primary consequences of this theory are exposed in Chapter 8: aspects of Poincaré's last geometric theorem and the Arnol'd conjecture are introduced. In Chapter 7 elements of the global asymptotic treatment of the highly oscillating integrals for the Schrödinger equation are discussed: as is well known, this eventually leads to the theory of Fourier Integral Operators. This short handbook is directed toward graduate students in Mathematics and Physics and to all those who desire a quick introduction to these beautiful subjects. |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN00125308 |
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Cardin, Franco
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| Cham, : Springer, : Unione Matematica Italiana, 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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Geometrical themes inspired by the N-body problem / Luis Hernández-Lamoneda, Haydeé Herrera, Rafael Herrera editors
| Geometrical themes inspired by the N-body problem / Luis Hernández-Lamoneda, Haydeé Herrera, Rafael Herrera editors |
| Pubbl/distr/stampa | [Cham], : Springer, 2018 |
| Descrizione fisica | VII, 125 p. : ill. ; 24 cm |
| Soggetto topico |
34Mxx - Ordinary differential equations in the complex domain [MSC 2020]
53C15 - General geometric structures on manifolds (almost complex, almost product structures, etc.) [MSC 2020] 70F07 - Three-body problem [MSC 2020] 57R58 - Floer homology [MSC 2020] 53D12 - Lagrangian submanifolds; Maslov index [MSC 2020] 37D15 - Morse-Smale systems [MSC 2020] |
| Soggetto non controllato |
Arnol'd conjecture for Hamiltonian diffeomorphisms
Complex differential equations Free homotopy classes of loops Isochronous solutions Lagrangian Floer homology McGehee transformation Morse theory N-body problem Ordinary differential equations |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN0117075 |
| [Cham], : Springer, 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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Geometrical themes inspired by the N-body problem / Luis Hernández-Lamoneda, Haydeé Herrera, Rafael Herrera editors
| Geometrical themes inspired by the N-body problem / Luis Hernández-Lamoneda, Haydeé Herrera, Rafael Herrera editors |
| Pubbl/distr/stampa | [Cham], : Springer, 2018 |
| Descrizione fisica | VII, 125 p. : ill. ; 24 cm |
| Soggetto topico |
34Mxx - Ordinary differential equations in the complex domain [MSC 2020]
37D15 - Morse-Smale systems [MSC 2020] 53C15 - General geometric structures on manifolds (almost complex, almost product structures, etc.) [MSC 2020] 53D12 - Lagrangian submanifolds; Maslov index [MSC 2020] 57R58 - Floer homology [MSC 2020] 70F07 - Three-body problem [MSC 2020] |
| Soggetto non controllato |
Arnol'd Conjecture for Hamiltonian Diffeomorphisms
Complex Differential Equations Free homotopy classes of loops Isochronous solutions Lagrangian Floer homology McGehee transformation Morse theory N-body Problem Ordinary differential equations |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN00117075 |
| [Cham], : Springer, 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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The hypoelliptic Laplacian and Ray-Singer metrics [[electronic resource] /] / Jean-Michel Bismut, Gilles Lebeau
| The hypoelliptic Laplacian and Ray-Singer metrics [[electronic resource] /] / Jean-Michel Bismut, Gilles Lebeau |
| Autore | Bismut Jean-Michel |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, : Princeton University Press, 2008 |
| Descrizione fisica | 1 online resource (378 p.) |
| Disciplina | 515/.7242 |
| Altri autori (Persone) | LebeauGilles |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Differential equations, Hypoelliptic
Laplacian operator Metric spaces |
| Soggetto non controllato |
Alexander Grothendieck
Analytic function Asymptote Asymptotic expansion Berezin integral Bijection Brownian dynamics Brownian motion Chaos theory Chern class Classical Wiener space Clifford algebra Cohomology Combination Commutator Computation Connection form Coordinate system Cotangent bundle Covariance matrix Curvature tensor Curvature De Rham cohomology Derivative Determinant Differentiable manifold Differential operator Dirac operator Direct proof Eigenform Eigenvalues and eigenvectors Ellipse Embedding Equation Estimation Euclidean space Explicit formula Explicit formulae (L-function) Feynman–Kac formula Fiber bundle Fokker–Planck equation Formal power series Fourier series Fourier transform Fredholm determinant Function space Girsanov theorem Ground state Heat kernel Hilbert space Hodge theory Holomorphic function Holomorphic vector bundle Hypoelliptic operator Integration by parts Invertible matrix Logarithm Malliavin calculus Martingale (probability theory) Matrix calculus Mellin transform Morse theory Notation Parameter Parametrix Parity (mathematics) Polynomial Principal bundle Probabilistic method Projection (linear algebra) Rectangle Resolvent set Ricci curvature Riemann–Roch theorem Scientific notation Self-adjoint operator Self-adjoint Sign convention Smoothness Sobolev space Spectral theory Square root Stochastic calculus Stochastic process Summation Supertrace Symmetric space Tangent space Taylor series Theorem Theory Torus Trace class Translational symmetry Transversality (mathematics) Uniform convergence Variable (mathematics) Vector bundle Vector space Wave equation |
| ISBN |
1-282-45837-X
9786612458378 1-4008-2906-2 |
| Classificazione | SK 620 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Introduction -- Chapter 1. Elliptic Riemann-Roch-Grothendieck and flat vector bundles -- Chapter 2. The hypoelliptic Laplacian on the cotangent bundle -- Chapter 3. Hodge theory, the hypoelliptic Laplacian and its heat kernel -- Chapter 4. Hypoelliptic Laplacians and odd Chern forms -- Chapter 5. The limit as t → +∞ and b → 0 of the superconnection forms -- Chapter 6. Hypoelliptic torsion and the hypoelliptic Ray-Singer metrics -- Chapter 7. The hypoelliptic torsion forms of a vector bundle -- Chapter 8. Hypoelliptic and elliptic torsions: a comparison formula -- Chapter 9. A comparison formula for the Ray-Singer metrics -- Chapter 10. The harmonic forms for b → 0 and the formal Hodge theorem -- Chapter 11. A proof of equation (8.4.6) -- Chapter 12. A proof of equation (8.4.8) -- Chapter 13. A proof of equation (8.4.7) -- Chapter 14. The integration by parts formula -- Chapter 15. The hypoelliptic estimates -- Chapter 16. Harmonic oscillator and the J0 function -- Chapter 17. The limit of A'2φb,±H as b → 0 -- Bibliography -- Subject Index -- Index of Notation |
| Record Nr. | UNINA-9910781084803321 |
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Bismut Jean-Michel
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| Princeton, : Princeton University Press, 2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Mathematical Tools for Neuroscience : A Geometric Approach / Richard A. Clement
| Mathematical Tools for Neuroscience : A Geometric Approach / Richard A. Clement |
| Autore | Clement, Richard A. |
| Pubbl/distr/stampa | Cham, : Springer, 2022 |
| Descrizione fisica | x, 162 p. : ill. ; 24 cm |
| Soggetto topico |
62P10 - Applications of statistics to biology and medical sciences; meta analysis [MSC 2020]
92-XX - Biology and other natural sciences [MSC 2020] 92B20 - Neural networks for/in biological studies, artificial life and related topics [MSC 2020] |
| Soggetto non controllato |
Arm Movements
Betti Numbers Colour Vision Delay Embedding Eye Movements Falling Cat Fibre Bundle Geodesic Hebbian Learning Heteroclinic Cycles Hopf bifurcation Morse theory Neural Integrator Slow-fast System Visual Cortex |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN0277885 |
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Clement, Richard A.
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| Cham, : Springer, 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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Mathematical Tools for Neuroscience : A Geometric Approach / Richard A. Clement
| Mathematical Tools for Neuroscience : A Geometric Approach / Richard A. Clement |
| Autore | Clement, Richard A. |
| Pubbl/distr/stampa | Cham, : Springer, 2022 |
| Descrizione fisica | x, 162 p. : ill. ; 24 cm |
| Soggetto topico |
62P10 - Applications of statistics to biology and medical sciences; meta analysis [MSC 2020]
92-XX - Biology and other natural sciences [MSC 2020] 92B20 - Neural networks for/in biological studies, artificial life and related topics [MSC 2020] |
| Soggetto non controllato |
Arm Movements
Betti Numbers Colour Vision Delay embedding Eye Movements Falling Cat Fibre Bundle Geodesic Hebbian Learning Heteroclinic Cycles Hopf bifurcation Morse theory Neural Integrator Slow-fast System Visual Cortex |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN00277885 |
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Clement, Richard A.
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| Cham, : Springer, 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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Morse homology with differential graded coefficients / Jean-François Barraud ... [et al.]
| Morse homology with differential graded coefficients / Jean-François Barraud ... [et al.] |
| Pubbl/distr/stampa | Cham, : Birkhäuser, 2025 |
| Descrizione fisica | 1 testo elettronico (xi, 229 p. : ill.) |
| Soggetto topico |
37D15 - Morse-Smale systems [MSC 2020]
55-XX - Algebraic topology [MSC 2020] 55N25 - Homology with local coefficients, equivariant cohomology [MSC 2020] 55T10 - Serre spectral sequences [MSC 2020] 57-XX - Manifolds and cell complexes [MSC 2020] 57R19 - Algebraic topology on manifolds and differential topology [MSC 2020] 57R58 - Floer homology [MSC 2020] |
| Soggetto non controllato |
Fibrations
Floer homotopy theory Floer theory Leray-Serre spectral sequence Morse homology Morse homology with DG coefficients Morse theory Poincaré duality Twisting cocycle |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN00309272 |
| Cham, : Birkhäuser, 2025 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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Morse theory and Floer homology / Michèle Audin, Mihai Damian ; translated by Reinie Erné
| Morse theory and Floer homology / Michèle Audin, Mihai Damian ; translated by Reinie Erné |
| Autore | Audin, Michele |
| Pubbl/distr/stampa | London, : Springer ; EDP sciences, 2014 |
| Descrizione fisica | XIV, 596 p. : ill. ; 24 cm |
| Altri autori (Persone) | Damian, Mihai |
| Soggetto topico |
53Dxx - Symplectic geometry, contact geometry [MSC 2020]
57R17 - Symplectic and contact topology in high or arbitrary dimension [MSC 2020] 53D40 - Symplectic aspects of Floer homology and cohomology [MSC 2020] 57R58 - Floer homology [MSC 2020] |
| Soggetto non controllato |
Arnold Conjecture
Floer Complex Floer homology Gluing Hamiltonian systems Maslov Index Morse Complex Morse Inequalities Morse homology Morse theory Symplectic Group Symplectic manifolds |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN0102533 |
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Audin, Michele
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| London, : Springer ; EDP sciences, 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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