混沌動力系統(tǒng)的概念和結果

內(nèi)容概要

　　《混沌動力系統(tǒng)的概念和結果》介紹了混沌動力系統(tǒng)的概念和其拓撲性質、雙曲率、不變測度、熵和其他概率結果。

書籍目錄

1  A Basic Problem
2  Dynamical Systems
  2.1  Basics of Mechanical Systems
  2.2  Formal Definitions
  2.3  Maps
  2.4  Basic Examples of Maps
  2.5  More Advanced Examples
  2.6  Examples of Flows
3  Topological Properties
  3.1  Coding, Kneading
  3.2  Topological Entropy
    3.2.1  Topological, Measure, and Metric Spaces
    3.2.2  Some Examples
    3.2.3  General Theory of Topological Entropy
    3.2.4  A Metric Version of Topological Entropy
  3.3  Attractors
4  Hyperbolicity
  4.1  Hyperbolic Fixed Points
    4.1.1  Stable and Unstable Manifolds
    4.1.2  Conjugation
    4.1.3  Resonances
  4.2  Invariant Manifolds
  4.3  Nonwandering Points and Axiom A Systems
  4.4  Shadowing and Its Consequences
    4.4.1  Sensitive Dependence on Initial Conditions
    4.4.2  Complicated Orbits Occur in Hyperbolic Systems
    4.4.3  Change of Map
  4.5  Construction of Markov Partitions
5  Invariant Measures
  5.1  Overview
  5.2  Details
  5.3  The Perron-Frobenius Operator
  5.4  The Ergodic Theorem
  5.5  Convergence Rates in the Ergodic Theorem
  5.6  Mixing and Decay of Correlations
  5.7  Physical Measures
  5.8  Lyapunov Exponents
6  Entropy
  6.1  The Shannon-McMillan-Breiman Theorem
  6.2  Sinai-Bowen-Ruelle Measures
  6.3  Dimensions
7  Statistics and Statistical Mechanics
  7.1  The Central Limit Theorem
  7.2  Large Deviations
  7.3  Exponential Estimates
  7.3. I  Concentration
  7.4  The Formalism of Statistical Mechanics
  7.5  Multifractal Measures
8  Other Probabilistic Results
  8.1  Entrance and Recurrence Times
  8.2  Number of Visits to a Set
  8.3  Extremes
  8.4  Quasi-lnvariant Measures
  8.5  Stochastic Perturbations
9  Experimental Aspects
  9.1  Correlation Functions and Power Spectrum
  9.2  Resonances
  9.3  Lyapunov Exponents
  9.4  Reconstruction
  9.5  Measuring the Lyapunov Exponents
  9.6  Measuring Dimensions
  9.7  Measuring Entropy
  9.8  Estimating the Invariant Measure
References
Index

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科萊和?？寺现摹痘煦鐒恿ο到y(tǒng)的概念和結果（影印版）》是“國外數(shù)學名著系列”之一，介紹了混沌動力系統(tǒng)的概念和其拓撲性質、雙曲率、不變測度、熵和其他概率結果。適合高等院校數(shù)學系研究生、數(shù)學科研人員學習參考。

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