導讀： 資源介紹 語言: 英文 地區: 德國 圖書fenlei: 科技 中文名: 拓撲動力系統概論 發行時間: 2005年 原名: Dynamical Systems 資源格式: DJVU 版本: 掃描版 簡介: djvu 閱讀器： http://windjview.sourceforge.n 資源介紹 語言: 英文 地區: 德國 圖書fenlei: 科技 中文名: 拓撲動力系統概論 發行時間: 2005年 原名: Dynamical Systems 資源格式: DJVU 版本: 掃描版 簡介:
djvu 閱讀器： http://windjview.sourceforge.net/
內容簡介：
基於對某些重要例子的嚴格分析，本書概述動力系統及其在復系統和其他領域研究中的意義。著重於動力系統中的不變量，如系統地論述Morse-Conley 理論，本書闡釋了動力系統中的基本數學概念。本書討論了熵及拓撲、度量、測度、光滑假設中與動力系統有關的概念，以及動力系統與信息論的某些聯系。本書還論述了細胞自動機和隨機布爾網絡等特殊例子。
內容截圖：
目錄: 1introduction .
2stability of dynamical systems, bifurcations, and generic
properties
21some general notions
22autonomous systems of odes
23examples: bifurcation depending on a paramet λεerr
24chaos in differential and difference equations the concept
of an attractor
25interaction, or the interplay between concentration or
reaction and diffusion
26discrete and continuous systems the poincare return map
27stability and bifurcations; generic properties
28the hopf bifurcation
29lotka-volterra equations
210 stable, unstable, and center manifolds
3discrete invariants of dynamical systems
31the topology of graphs
32floer homology..
33conley theory: examples and results
34cohomological conley index
.35homotopical invariants
36continuation properties of the conley index
37the discrete couley index
entropy and topological aspects of dynamical systems
41the entropy of a process as an asymptotic quantity
42positive entropy and chaos
43symbolic dynamics
entropy and metric aspects of dynamical systems
51the metric approach to topological entropy
52complexity and intrinsic scales
6entropy and measure theoretic aspects of dynamical
systems
61probability spaces and measure preserving maps
62ergodicity
63entropy and information
64invariant measures
65stochastic processes
66stochastic bifurcations
smooth dynamical systems
71lyapunov exponents
72hyperbolicity
73information loss
cellular automata and boolean networks as examples of
discrete dynamical systems
81cellular automata
82boolean networks
references
index.