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內容簡介

　　基於對某些重要例子的嚴格分析，《國外數學名著係列7（影印版）：動力係統》概述動力係統及其在復係統和其他領域研究中的意義。著重於動力係統中的不變量，如係統地論述Morse-Conley理論，《國外數學名著係列7（影印版）：動力係統》闡釋瞭動力係統中的基本數學概念。
　　《國外數學名著係列7（影印版）：動力係統》討論瞭熵及拓撲、度量、測度、光滑假設中與動力係統有關的概念，以及動力係統與信息論的某些聯係。
　　《國外數學名著係列7（影印版）：動力係統》還論述瞭細胞自動機和隨機布爾網絡等特殊例子。

內頁插圖

目錄

1 Introduction

2 Stability of dynamical systems bifurcations and generic properties
2．1 Some general notions
2．2 Autonomous systems of ODEs
2．3 Examples： Bifurcation depending on a parameter
2．4 Chaos in differential and difference equations． The concept of an attractor
2．5 Interaction or the interplay between concentration or reaction and diffusion
2．6 Discrete and continuous systems． The Poincare return map
2．7 Stability and bifurcations; generic properties
2．8 The Hopf bifurcation
2．9 Lotka-Volterra equations
2．10 Stable unstable and center manifolds

3 Discrete invariants of dynamical systems
3．1 The topology of graphs
3．2 Floer homology
3．3 Conley theory： examples and results
3．4 Cohomological Conley index
3．5 Homotopical invariants
3．6 Continuation properties of the Conley index
3．7 The discrete Conley index

4 Entropy and topological aspects of dynamical systems
4．1 The entropy of a process as an asymptotic quantity
4．2 Positive entropy and chaos
4．3 Symbolic dynamics

5 Entropy and metric aspects of dynamical systems
5．1 The metric approach to topological entropy
5．2 Complexity and intrinsic scales

6 Entropy and measure theoretic aspects of dynamical systems
6．1 Probability spaces and measure preserving maps
6．2 Ergodicity
6．3 Entropy and information
6．4 Invariant measures
6．5 Stochastic processes
6．6 Stochastic bifurcations

7 Smooth dynamical systems
7．1 Lyapunov exponents
7．2 Hyperbolicity
7．3 Information loss

8 Cellular automata and Boolean networks as examples of discrete dynamical systems
8．1 Cellular automata
8．2 Boolean networks

References
Index

前言/序言

國外數學名著係列7（影印版）：動力係統 [Dynamical Systems] 下載 mobi epub pdf txt 電子書

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