Chaotic transitions in deterministic and stochastic dynamical systems : applications of Melnikov processes in engineering, physics, and neuroscience / / Emil Simiu |
Autore | Simiu Emil |
Pubbl/distr/stampa | Princeton, New Jersey : , : Princeton University Press, , 2002 |
Descrizione fisica | 1 online resource (244 p.) |
Disciplina | 515/.352 |
Collana | Princeton Series in Applied Mathematics |
Soggetto topico |
Differentiable dynamical systems
Chaotic behavior in systems Stochastic systems |
Soggetto non controllato |
Affine transformation
Amplitude Arbitrarily large Attractor Autocovariance Big O notation Central limit theorem Change of variables Chaos theory Coefficient of variation Compound Probability Computational problem Control theory Convolution Coriolis force Correlation coefficient Covariance function Cross-covariance Cumulative distribution function Cutoff frequency Deformation (mechanics) Derivative Deterministic system Diagram (category theory) Diffeomorphism Differential equation Dirac delta function Discriminant Dissipation Dissipative system Dynamical system Eigenvalues and eigenvectors Equations of motion Even and odd functions Excitation (magnetic) Exponential decay Extreme value theory Flow velocity Fluid dynamics Forcing (recursion theory) Fourier series Fourier transform Fractal dimension Frequency domain Gaussian noise Gaussian process Harmonic analysis Harmonic function Heteroclinic orbit Homeomorphism Homoclinic orbit Hyperbolic point Inference Initial condition Instability Integrable system Invariant manifold Iteration Joint probability distribution LTI system theory Limit cycle Linear differential equation Logistic map Marginal distribution Moduli (physics) Multiplicative noise Noise (electronics) Nonlinear control Nonlinear system Ornstein–Uhlenbeck process Oscillation Parameter space Parameter Partial differential equation Perturbation function Phase plane Phase space Poisson distribution Probability density function Probability distribution Probability theory Probability Production–possibility frontier Relative velocity Scale factor Shear stress Spectral density Spectral gap Standard deviation Stochastic process Stochastic resonance Stochastic Stream function Surface stress Symbolic dynamics The Signal and the Noise Topological conjugacy Transfer function Variance Vorticity |
ISBN |
0-691-05094-5
1-4008-3250-0 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Front matter -- Contents -- Preface -- Chapter 1. Introduction -- PART 1. FUNDAMENTALS -- Chapter 2. Transitions in Deterministic Systems and the Melnikov Function -- Chapter 3. Chaos in Deterministic Systems and the Melnikov Function -- Chapter 4. Stochastic Processes -- Chapter 5. Chaotic Transitions in Stochastic Dynamical Systems and the Melnikov Process -- PART 2. APPLICATIONS -- Chapter 6. Vessel Capsizing -- Chapter 7. Open-Loop Control of Escapes in Stochastically Excited Systems -- Chapter 8. Stochastic Resonance -- Chapter 9. Cutoff Frequency of Experimentally Generated Noise for a First-Order Dynamical System -- Chapter 10. Snap-Through of Transversely Excited Buckled Column -- Chapter 11. Wind-Induced Along-Shore Currents over a Corrugated Ocean Floor -- Chapter 12. The Auditory Nerve Fiber as a Chaotic Dynamical System -- Appendix A1 Derivation of Expression for the Melnikov Function -- Appendix A2 Construction of Phase Space Slice through Stable and Unstable Manifolds -- Appendix A3 Topological Conjugacy -- Appendix A4 Properties of Space ∑2 -- Appendix A5 Elements of Probability Theory -- Appendix A6 Mean Upcrossing Rate τu-1 for Gaussian Processes -- Appendix A7 Mean Escape Rate τ∊-1 for Systems Excited by White Noise -- References -- Index |
Record Nr. | UNINA-9910786748903321 |
Simiu Emil
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Princeton, New Jersey : , : Princeton University Press, , 2002 | ||
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Lo trovi qui: Univ. Federico II | ||
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Chaotic transitions in deterministic and stochastic dynamical systems : applications of Melnikov processes in engineering, physics, and neuroscience / / Emil Simiu |
Autore | Simiu Emil |
Pubbl/distr/stampa | Princeton, New Jersey : , : Princeton University Press, , 2002 |
Descrizione fisica | 1 online resource (244 p.) |
Disciplina | 515/.352 |
Collana | Princeton Series in Applied Mathematics |
Soggetto topico |
Differentiable dynamical systems
Chaotic behavior in systems Stochastic systems |
Soggetto non controllato |
Affine transformation
Amplitude Arbitrarily large Attractor Autocovariance Big O notation Central limit theorem Change of variables Chaos theory Coefficient of variation Compound Probability Computational problem Control theory Convolution Coriolis force Correlation coefficient Covariance function Cross-covariance Cumulative distribution function Cutoff frequency Deformation (mechanics) Derivative Deterministic system Diagram (category theory) Diffeomorphism Differential equation Dirac delta function Discriminant Dissipation Dissipative system Dynamical system Eigenvalues and eigenvectors Equations of motion Even and odd functions Excitation (magnetic) Exponential decay Extreme value theory Flow velocity Fluid dynamics Forcing (recursion theory) Fourier series Fourier transform Fractal dimension Frequency domain Gaussian noise Gaussian process Harmonic analysis Harmonic function Heteroclinic orbit Homeomorphism Homoclinic orbit Hyperbolic point Inference Initial condition Instability Integrable system Invariant manifold Iteration Joint probability distribution LTI system theory Limit cycle Linear differential equation Logistic map Marginal distribution Moduli (physics) Multiplicative noise Noise (electronics) Nonlinear control Nonlinear system Ornstein–Uhlenbeck process Oscillation Parameter space Parameter Partial differential equation Perturbation function Phase plane Phase space Poisson distribution Probability density function Probability distribution Probability theory Probability Production–possibility frontier Relative velocity Scale factor Shear stress Spectral density Spectral gap Standard deviation Stochastic process Stochastic resonance Stochastic Stream function Surface stress Symbolic dynamics The Signal and the Noise Topological conjugacy Transfer function Variance Vorticity |
ISBN |
0-691-05094-5
1-4008-3250-0 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Front matter -- Contents -- Preface -- Chapter 1. Introduction -- PART 1. FUNDAMENTALS -- Chapter 2. Transitions in Deterministic Systems and the Melnikov Function -- Chapter 3. Chaos in Deterministic Systems and the Melnikov Function -- Chapter 4. Stochastic Processes -- Chapter 5. Chaotic Transitions in Stochastic Dynamical Systems and the Melnikov Process -- PART 2. APPLICATIONS -- Chapter 6. Vessel Capsizing -- Chapter 7. Open-Loop Control of Escapes in Stochastically Excited Systems -- Chapter 8. Stochastic Resonance -- Chapter 9. Cutoff Frequency of Experimentally Generated Noise for a First-Order Dynamical System -- Chapter 10. Snap-Through of Transversely Excited Buckled Column -- Chapter 11. Wind-Induced Along-Shore Currents over a Corrugated Ocean Floor -- Chapter 12. The Auditory Nerve Fiber as a Chaotic Dynamical System -- Appendix A1 Derivation of Expression for the Melnikov Function -- Appendix A2 Construction of Phase Space Slice through Stable and Unstable Manifolds -- Appendix A3 Topological Conjugacy -- Appendix A4 Properties of Space ∑2 -- Appendix A5 Elements of Probability Theory -- Appendix A6 Mean Upcrossing Rate τu-1 for Gaussian Processes -- Appendix A7 Mean Escape Rate τ∊-1 for Systems Excited by White Noise -- References -- Index |
Record Nr. | UNINA-9910827211303321 |
Simiu Emil
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Princeton, New Jersey : , : Princeton University Press, , 2002 | ||
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Lo trovi qui: Univ. Federico II | ||
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Degree of Approximation by Polynomials in the Complex Domain. (AM-9), Volume 9 / / Walter Edwin Sewell |
Autore | Sewell Walter Edwin |
Pubbl/distr/stampa | Princeton, NJ : , : Princeton University Press, , [2016] |
Descrizione fisica | 1 online resource (252 pages) |
Disciplina | 512.22 |
Collana | Annals of Mathematics Studies |
Soggetto topico |
Approximation theory
Polynomials |
Soggetto non controllato |
0B
Addition Antiderivative Approximation Arbitrarily large Arc (geometry) Arc length Big O notation Bijection Bounded set (topological vector space) Branch point Circumference Coefficient Complex analysis Complex number Conformal map Connected space Constant of integration Continuous function Covering space Derivative Difference "ient Differentiable function Dimension Elementary proof Equation Even and odd functions Existence theorem Existential quantification Exterior (topology) Floor and ceiling functions Fourier series Function of a real variable Geometry Green's function Harmonic function Harmonic polynomial Infimum and supremum Infinitesimal Integer Isolated point Isolated singularity Iterative method Jordan curve theorem Least squares Lebesgue integration Lemniscate Limit (mathematics) Line integral Line segment Lipschitz continuity Logarithm Mathematician Modulus of continuity Natural number Notation Open problem Orthogonal polynomials Partial derivative Periodic function Point at infinity Polynomial Rational function Real variable Rectangle Requirement Riemann sum Root of unity Second derivative Set theory Sign (mathematics) Simply connected space Special case Suggestion Summation Surface integral Taylor series Theorem Theory Trigonometric functions Trigonometry Uniform convergence Unit circle Upper and lower bounds Variable (mathematics) Weight function |
ISBN | 1-4008-8221-4 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Frontmatter -- Preface -- Contents -- Chapter I. Preliminaries -- Part I. Problem α -- Chapter II. Polynomial Inequalities -- Chapter III. Tchebycheff Approximation -- Chapter IV. Approximation Measured by a Line Integral -- Part II. Problem β -- Chapter V. Preliminaries -- Chapter VI. Tchebycheff Approximation -- Chapter VII. Approximation Measured by a Line Integral -- Chapter VIII. Special Configurations -- Bibliography |
Record Nr. | UNINA-9910154748503321 |
Sewell Walter Edwin
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Princeton, NJ : , : Princeton University Press, , [2016] | ||
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Lo trovi qui: Univ. Federico II | ||
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Isoperimetric Inequalities in Mathematical Physics. (AM-27), Volume 27 / / G. Szegö, G. Polya |
Autore | Polya G. |
Pubbl/distr/stampa | Princeton, NJ : , : Princeton University Press, , [2016] |
Descrizione fisica | 1 online resource (296 pages) |
Disciplina | 530.151 |
Collana | Annals of Mathematics Studies |
Soggetto topico |
Isoperimetric inequalities
Mathematical physics |
Soggetto non controllato |
Approximation error
Approximation Arc (geometry) Arithmetic mean Axiom Bessel function Big O notation Biharmonic equation Boundary value problem Bounded set (topological vector space) Calculation Calculus of variations Cartesian coordinate system Coefficient Complex number Complex plane Computation Conformal map Conjecture Conservative vector field Convex curve Convex set Cylinder (geometry) Degeneracy (mathematics) Differential equation Differential geometry of surfaces Dirichlet integral Dirichlet problem Dirichlet's principle Dodecahedron Eigenfunction Eigenvalues and eigenvectors Electrostatics Elliptic integral Equation Equilateral triangle Even and odd functions Existence theorem Explicit formulae (L-function) Exterior (topology) Fourier series Function (mathematics) Gaussian curvature Geometric progression Harmonic function Homogeneous coordinates Hypotenuse Intersection (set theory) Isoperimetric inequality Isoperimetric problem Linear function Markov chain Mathematical physics Mathematical proof Mathematician Mathematics Maxima and minima Monotonic function Numerical analysis Parallelogram Parametric equation Partial derivative Partial differential equation Partial fraction decomposition Periodic function Poincaré conjecture Point at infinity Polar moment of inertia Polyhedron Polynomial Potential theory Power series Projection (linear algebra) Proportionality (mathematics) Quadratic form Quantity Rectangle Regular polygon Rhombus Riemann surface Scientific notation Semi-major and semi-minor axes Series (mathematics) Sign (mathematics) Simply connected space Special case Spheroid Stress functions Summation Symmetrization Tetrahedron Theorem Three-dimensional space (mathematics) Trigonometric functions Two-dimensional space Unit sphere Upper and lower bounds Vanish at infinity Variable (mathematics) Variational method (quantum mechanics) |
ISBN | 1-4008-8266-4 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Frontmatter -- PREFACE -- TABLE OF CONTENTS -- CHAPTER I. DEFINITIONS, METHODS AND RESULTS -- CHAPTER II. THE PRINCIPLES OP DIRICHLET AND THOMSON -- CHAPTER III. APPLICATIONS OP THE PRINCIPLES OP DIRICHLET AND THOMSON TO ESTIMATION OP THE CAPACITY -- CHAPTER IV. CIRCULAR PLATE CONDENSER -- CHAPTER V. TORSIONAL RIGIDITY AND PRINCIPAL FREQUENCY -- CHAPTER VI. NEARLY CIRCULAR AND NEARLY SPHERICAL DOMAINS -- CHAPTER VIII. ON ELLIPSOID AND LENS -- NOTE A. SURFACE-AREA AND DIRICHLET'S INTEGRAL -- NOTE B. ON CONTINUOUS SYMMETRIZATION -- NOTE C. ON SPHERICAL SYMMETRIZATION -- NOTE D. ON A GENERALIZATION OF DIRICHLET'S INTEGRAL -- NOTE E. HEAT-CONDUCTION ON A SURFACE -- NOTE F. ON MEMBRANES AND PLATES -- NOTE G. VIRTUAL MASS AND POLARIZATION -- TABLES FOR SOME SET-FUNCTIONS OF PLANE DOMAINS -- BIBLIOGRAPHY -- LIST OF SYMBOLS |
Record Nr. | UNINA-9910154747803321 |
Polya G.
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Princeton, NJ : , : Princeton University Press, , [2016] | ||
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Lo trovi qui: Univ. Federico II | ||
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Radon transforms and the rigidity of the Grassmannians [[electronic resource] /] / Jacques Gasqui and Hubert Goldschmidt |
Autore | Gasqui Jacques |
Edizione | [Course Book] |
Pubbl/distr/stampa | Princeton, N.J., : Princeton University Press, 2004 |
Descrizione fisica | 1 online resource (385 p.) |
Disciplina | 515/.723 |
Altri autori (Persone) | GoldschmidtHubert <1942-> |
Collana | Annals of mathematics studies |
Soggetto topico |
Radon transforms
Grassmann manifolds |
Soggetto non controllato |
Adjoint
Automorphism Cartan decomposition Cartan subalgebra Casimir element Closed geodesic Cohomology Commutative property Complex manifold Complex number Complex projective plane Complex projective space Complex vector bundle Complexification Computation Constant curvature Coset Covering space Curvature Determinant Diagram (category theory) Diffeomorphism Differential form Differential geometry Differential operator Dimension (vector space) Dot product Eigenvalues and eigenvectors Einstein manifold Elliptic operator Endomorphism Equivalence class Even and odd functions Exactness Existential quantification G-module Geometry Grassmannian Harmonic analysis Hermitian symmetric space Hodge dual Homogeneous space Identity element Implicit function Injective function Integer Integral Isometry Killing form Killing vector field Lemma (mathematics) Lie algebra Lie derivative Line bundle Mathematical induction Morphism Open set Orthogonal complement Orthonormal basis Orthonormality Parity (mathematics) Partial differential equation Projection (linear algebra) Projective space Quadric Quaternionic projective space Quotient space (topology) Radon transform Real number Real projective plane Real projective space Real structure Remainder Restriction (mathematics) Riemann curvature tensor Riemann sphere Riemannian manifold Rigidity (mathematics) Scalar curvature Second fundamental form Simple Lie group Standard basis Stokes' theorem Subgroup Submanifold Symmetric space Tangent bundle Tangent space Tangent vector Tensor Theorem Topological group Torus Unit vector Unitary group Vector bundle Vector field Vector space X-ray transform Zero of a function |
ISBN |
1-282-15898-8
9786612158988 1-4008-2617-9 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- Chapter I. Symmetric Spaces and Einstein Manifolds -- Chapter II. Radon Transforms on Symmetric Spaces -- Chapter III. Symmetric Spaces of Rank One -- Chapter IV. The Real Grassmannians -- Chapter V. The Complex Quadric -- Chapter VI. The Rigidity of the Complex Quadric -- Chapter VII. The Rigidity of the Real Grassmannians -- Chapter VIII. The Complex Grassmannians -- Chapter IX. The Rigidity of the Complex Grassmannians -- Chapter X. Products of Symmetric Spaces -- References -- Index |
Record Nr. | UNINA-9910778216403321 |
Gasqui Jacques
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Princeton, N.J., : Princeton University Press, 2004 | ||
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Lo trovi qui: Univ. Federico II | ||
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Scattering Theory for Automorphic Functions. (AM-87), Volume 87 / / Peter D. Lax, Ralph S. Phillips |
Autore | Lax Peter D. |
Pubbl/distr/stampa | Princeton, NJ : , : Princeton University Press, , [2016] |
Descrizione fisica | 1 online resource (313 pages) |
Disciplina | 515.9 |
Collana | Annals of Mathematics Studies |
Soggetto topico |
Automorphic functions
Scattering (Mathematics) |
Soggetto non controllato |
Absolute continuity
Algebra Analytic continuation Analytic function Annulus (mathematics) Asymptotic distribution Automorphic function Bilinear form Boundary (topology) Boundary value problem Bounded operator Calculation Cauchy sequence Change of variables Complex plane Conjugacy class Convolution Cusp neighborhood Cyclic group Derivative Differential equation Differential operator Dimension (vector space) Dimensional analysis Dirichlet integral Dirichlet series Eigenfunction Eigenvalues and eigenvectors Eisenstein series Elliptic operator Elliptic partial differential equation Equation Equivalence class Even and odd functions Existential quantification Explicit formula Explicit formulae (L-function) Exponential function Fourier transform Function space Functional analysis Functional calculus Fundamental domain Harmonic analysis Hilbert space Hyperbolic partial differential equation Infinitesimal generator (stochastic processes) Integral equation Integration by parts Invariant subspace Laplace operator Laplace transform Lebesgue measure Linear differential equation Linear space (geometry) Matrix (mathematics) Maximum principle Meromorphic function Modular group Neumann boundary condition Norm (mathematics) Null vector Number theory Operator theory Orthogonal complement Orthonormal basis Paley–Wiener theorem Partial differential equation Perturbation theory (quantum mechanics) Perturbation theory Primitive element (finite field) Principal component analysis Projection (linear algebra) Quadratic form Removable singularity Representation theorem Resolvent set Riemann hypothesis Riemann surface Riemann zeta function Riesz representation theorem Scatter matrix Scattering theory Schwarz reflection principle Selberg trace formula Self-adjoint Semigroup Sign (mathematics) Spectral theory Subgroup Subsequence Summation Support (mathematics) Theorem Trace class Trace formula Unitary operator Wave equation Weighted arithmetic mean Winding number |
ISBN | 1-4008-8156-0 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Frontmatter -- TABLE OF CONTENTS -- PREFACE -- LIST OF SYMBOLS -- §1. INTRODUCTION -- §2. AN ABSTRACT SCATTERING THEORY -- §3. A MODIFIED THEORY FOR SECOND ORDER EQUATIONS WITH AN INDEFINITE ENERGY FORM -- §4. THE LAPLACE-BELTRAMI OPERATOR FOR THE MODULAR GROUP -- §5. THE AUTOMORPHIC WAVE EQUATIONS -- §6. INCOMING AND OUTGOING SUBSPACES FOR THE AUTOMORPHIC WAVE EQUATION -- §7. THE SCATTERING MATRIX FOR THE AUTOMORPHIC WAVE EQUATION -- §8. THE GENERAL CASE -- §9. THE SELBERG TRACE FORMULA -- REFERENCES -- INDEX -- Backmatter |
Record Nr. | UNINA-9910154746703321 |
Lax Peter D.
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Princeton, NJ : , : Princeton University Press, , [2016] | ||
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Lo trovi qui: Univ. Federico II | ||
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Stable and Random Motions in Dynamical Systems : With Special Emphasis on Celestial Mechanics (AM-77) / / Jurgen Moser |
Autore | Moser Jurgen |
Edizione | [With a New foreword by Philip J. Holmes] |
Pubbl/distr/stampa | Princeton, NJ : , : Princeton University Press, , [2016] |
Descrizione fisica | 1 online resource (212 pages) : illustrations |
Disciplina | 521/.1 |
Collana | Princeton Landmarks in Mathematics and Physics |
Soggetto topico | Celestial mechanics |
Soggetto non controllato |
Accuracy and precision
Action-angle coordinates Analytic function Bounded variation Calculation Chaos theory Coefficient Commutator Constant term Continuous embedding Continuous function Coordinate system Countable set Degrees of freedom (statistics) Degrees of freedom Derivative Determinant Differentiable function Differential equation Dimension (vector space) Discrete group Divergent series Divisor Duffing equation Eigenfunction Eigenvalues and eigenvectors Elliptic orbit Energy level Equation Ergodic theory Ergodicity Euclidean space Even and odd functions Existence theorem Existential quantification First-order partial differential equation Forcing function (differential equations) Fréchet derivative Gravitational constant Hamiltonian mechanics Hamiltonian system Hessian matrix Heteroclinic orbit Homoclinic orbit Hyperbolic partial differential equation Hyperbolic set Initial value problem Integer Integrable system Integration by parts Invariant manifold Inverse function Invertible matrix Iteration Jordan curve theorem Klein bottle Lie algebra Linear map Linear subspace Linearization Maxima and minima Monotonic function Newton's method Nonlinear system Normal bundle Normal mode Open set Parameter Partial differential equation Periodic function Periodic point Perturbation theory (quantum mechanics) Phase space Poincaré conjecture Polynomial Probability theory Proportionality (mathematics) Quasiperiodic motion Rate of convergence Rational dependence Regular element Root of unity Series expansion Sign (mathematics) Smoothness Special case Stability theory Statistical mechanics Structural stability Symbolic dynamics Symmetric matrix Tangent space Theorem Three-body problem Uniqueness theorem Unitary matrix Variable (mathematics) Variational principle Vector field Zero of a function |
ISBN | 1-4008-8269-9 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Frontmatter -- TABLE OF CONTENTS -- I. INTRODUCTION -- II. STABILITY PROBLEMS -- III. STATISTICAL BEHAVIOR -- V. FINAL REMARKS -- V. EXISTENCE PROOF IN THE PRESENCE OF SMALL DIVISORS -- VI. PROOFS AND DETAILS FOR CHAPTER III -- BOOKS AND SURVEY ARTICLES |
Record Nr. | UNINA-9910164944903321 |
Moser Jurgen
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Princeton, NJ : , : Princeton University Press, , [2016] | ||
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Lo trovi qui: Univ. Federico II | ||
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