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Band 245

Ergodic Theory

Aus der Reihe Grundlehren der mathematischen Wissenschaften

107,99 €

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

14.06.2012

Verlag

Springer Us

Seitenzahl

486

Maße (L/B/H)

23,5/15,5/2,7 cm

Gewicht

759 g

Auflage

Nachdr. d. Ausg. v. 1982

Übersetzt von

A. B. Sossinskii

Sprache

Englisch

ISBN

978-1-4615-6929-9

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

14.06.2012

Verlag

Springer Us

Seitenzahl

486

Maße (L/B/H)

23,5/15,5/2,7 cm

Gewicht

759 g

Auflage

Nachdr. d. Ausg. v. 1982

Übersetzt von

A. B. Sossinskii

Sprache

Englisch

ISBN

978-1-4615-6929-9

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: ProductSafety@springernature.com

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  • Produktbild: Ergodic Theory
  • Produktbild: Ergodic Theory
  • I Ergodicity and Mixing. Examples of Dynamic Systems.- 1 Basic Definitions of Ergodic Theory.-
    1. Definition of Dynamical Systems.-
    2. The Birkhoff-Khinchin Ergodic Theorem. Ergodicity.-
    3. Nonergodic Systems. Decomposition into Ergodic Components.-
    4. Averaging in the Ergodic Case.-
    5. Integral and Induced Automorphisms.-
    6. Weak Mixing, Mixing, Multiple Mixing.-
    7. Unitary and Isometric Operators Adjoint to Dynamical Systems.-
    8. Dynamical Systems on Compact Metric Spaces.- 2 Smooth Dynamical Systems on Smooth Manifolds.-
    1. Invariant Measures Compatible with Differentiability.-
    2. Liouville’s Theorem and the Dynamical Systems of Classical Mechanics.-
    3. Integrable Dynamical Systems.- 3 Smooth Dynamical Systems on the Torus.-
    1. Translations on the Torus.-
    2. The Lagrange Problem.-
    3. Homeomorphisms of the Circle.-
    4. The Denjoy Theorem.-
    5. Arnold’s Example.-
    6. The Ergodicity of Diffeomorphisms of the Circle with Respect to Lebesgue Measure.- 4 Dynamical Systems of Algebraic Origin.-
    1. Translations on Compact Topological Groups.-
    2. Skew Translations and Compound Skew Translations on Commutative Compact Groups.-
    3. Endomorphisms and Automorphisms of Commutative Compact Groups.-
    4. Dynamical Systems on Homogenous Spaces of the Group SL(2, ?).- 5 Interval Exchange Transformations.-
    1. Definition of Interval Exchange Transformations.-
    2. An Estimate of the Number of Invariant Measures.-
    3. Absence of Mixing.-
    4. An Example of a Minimal but not Uniquely Ergodic Interval Exchange Transformation.- 6 Billiards.-
    1. The Construction of Dynamical Systems of the Billiards Type.-
    2. Billiards in Polygons and Polyhedra.-
    3. Billiards in Domains with Convex Boundary.-
    4. Systems of One-dimensional Point-like Particles.-
    5. Lorentz Gas and Systems of Hard Spheres.- 7 Dynamical Systems in Number Theory.-
    1. Uniform Distribution.-
    2. Uniform Distribution of Fractional Parts of Polynomials.-
    3. Uniform Distribution of Fractional Parts of Exponential Functions.-
    4. Ergodic Properties of Decompositions into Continuous Tractions and Piecewise-monotonic Maps.- 8 Dynamical Systems in Probability Theory.-
    1. Stationary Random Processes and Dynamical Systems.-
    2. Gauss Dynamical Systems.- 9 Examples of Infinite Dimensional Dynamical Systems.-
    1. Ideal Gas.-
    2. Dynamical Systems of Statistical Mechanics.-
    3. Dynamical Systems and Partial Differential Equations.- II Basic Constructions of Ergodic Theory.- 10 Simplest General Constructions and Elements of Entropy Theory of Dynamical Systems.-
    1. Direct and Skew Products of Dynamical Systems.-
    2. Metric Isomorphism of Skew Products. Equivalence of Dynamical Systems in the Sense of Kakutani.-
    3. Time Change in Flows.-
    4. Endomorphisms and Their Natural Extensions.-
    5. The Rohlin-Halmos Lemma.-
    6. Entropy.-
    7. Metric Isomorphism of Bernoulli Automorphisms.-
    8. K-systems and Exact Endomorphisms.- 11 Special Representations of Flows.-
    1. Definition of Special Flows.-
    2. Statement of the Main Theorem on Special Representation of Flows and Examples of Special Flows.-
    3. Proof of the Theorem on Special Representation.-
    4. Rudolph’s Theorem.- III Spectral Theory of Dynamical Systems.- 12 Dynamical Systems with Pure Point Spectrum.-
    1. General Properties of Eigen-Values and Eigen-Functions of Dynamical Systems.-
    2. Dynamical Systems with Pure Point Spectrum. The Case of Discrete Time.-
    3. Dynamical Systems with Pure Point Spectrum. The Case of Continuous Time.- 13 Examples of Spectral Analysis of Dynamical Systems.-
    1. Spectra of K-automorphisms.-
    2. Spectra of Ergodic Automorphisms of Commutative Compact Groups.-
    3. Spectra of Compound Skew Translations on the Torus and of Their Perturbations.-
    4. Examples of the Spectral Analysis of Automorphisms with Singular Spectrum.-
    5. Spectra of K-flows.- 14 Spectral Analysis of Gauss Dynamical Systems.-
    1. The Decomposition of Hilbert Space L2(M, 𝔖, µ) into Hermite-Ito Polynomial Subspaces.-
    2. Ergodicity and Mixing Criteria for Gauss Dynamical Systems.-
    3. The Maximal Spectral Type of Unitary Operators Adjoint to Gauss Dynamical Systems.-
    4. Gauss Dynamical Systems with Simple Continuous Spectrum.-
    5. Gauss Dynamical Systems with Finite Multiplicity Spectrum.- IV Approximation Theory of Dynamical Systems by Periodic Dynamical Systems and Some of its Applications.- 15 Approximations of Dynamical Systems.-
    1. Definition and Types of Approximations. Ergodicity and Mixing Conditions.-
    2. Approximations and Spectra.-
    3. An Application of Approximation Theory: an Example of an Ergodic Automorphism with a Spectrum Lacking the Group Property.-
    4. Approximation of Flows.- 16 Special Representations and Approximations of Smooth Dynamical Systems on the Two-dimensional Torus.-
    1. Special Representations of Flows on the Torus.-
    2. Dynamical Systems with Pure Point Spectrum on the Two-dimensional Torus.-
    3. Approximations of Flows on the Torus.-
    4. Example of a Smooth Flow with Continuous Spectrum on the Two-dimensional Torus.- Appendix 1.- Lebesgue Spaces and Measurable Partitions.- Appendix 2.- Relevant Facts from the Spectral Theory of Unitary Operators.- Appendix 3.- Proof of the Birkhoff-Khinchin Theorem.- Appendix 4.- Kronecker Sets.- Bibliographical Notes.