动力系统

出版时间：2006-1  出版社：科学出版社  作者：Jurgen Jost  页数：189  字数：231000  
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内容概要

基于对某些重要例子的严格分析，本书概述动力系统及其在复系统和其他领域研究中的意义。着重于动力系统中的不变量，如系统地论述Morse—Conley理论，本书阐释了动力系统中的基本数学概念。本书讨论了熵及拓扑、度量、测度、光滑假设中与动力系统有关的概念，以及动力系统与信息论的某些联系。本书还论述了细胞自动机和随机布尔网络等特殊例子。

书籍目录

1 Introduction2 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 manifolds3 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 index4 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 dynamics5 Entropy and metric aspects of dynamical systems  5.1 the metric approach to topological entropy  5.2 Complexity and intrinsic scales6 Entropy and measure theoretic aspects of dynamical systems  6.1 Probabolity spaces and measure preserving maps  6.2 Ergodicity  6.3 Entropy and information  6.4 Invariant measures  6.5 Stochastic processes  6.6 Stochastic bifurcations7 Smooth dynamical systems  7.1 Lyapunov exponents  7.2 Hyperbolicity  7.3 Information loss8 Cellular automata and Boolean networks as examples of discrete dynamical systems  8.1 Cellular automata  8.2 boolean networksReferencesIndex

用户评论 (总计1条)

•   觉得书中的数学符号不常见，有没有专门注释符号。不推荐。