作者：陈功
页数：307
出版社：哈尔滨工业大学出版社
出版日期：2021
ISBN：9787560394268
电子书格式：pdf/epub/txt
内容简介
本书是一本版权引进的英文版非线性科学的教程,这本书的内容是由作者所教授的动力学系统和混沌的研究生入门课程的课堂讲稿组成.本书正文共分十章,介绍了有限维空间混沌映射的基本理论.主题包括一维动力系统(区间映射)、分歧、一般拓扑、符号动力系统、分形和一类由区间映射导出的无限维动力系统,以及混沌映射的快速涨落,这是作者近年来提出的新观点。
目录
Preface
1 Simple Interval Maps and Their Iterations
1.1 Introduction
1.2 The Inverse and hnplicit Function Theorems
1.3 Visualizing from the Graphics oflterations of the Quadratic Map
Notes for Chapter 1
2 Total Variations of Iterates of Maps
2.1 The Use of Total Variations as a Measure of Chaos
Notes for Chapter 2
3 Ordering among Periods: The Sharkovski Theorem
Notes for Chapter 3
4 Bifurcation Theorems for Maps
4.1 The Period-Doubling Bifurcation Theorem
4.2 Saddle-Node Bifurcations
4.3 The Pitchfork Bifurcation
4.4 Hopf Bifurcation
Notes for Chapter 4
5 Homoclinicity. LyapunoffExponents
5.1 Homoclinic Orbits
5.2 Lyapunoff Exponents
Notes for Chapter 5
6 Symbolic Dynamics, Conjugacy and Shift Invariant Sets
6.1 The Itinerary of an Orbit
6.2 Properties of the shift map σ
6.3 Symbolic Dynamical Systems Σk and Σk+
6.4 The Dynamics of (Σl+，σ+) and Chaos
6.5 Topological Conjugacy and Semiconjugacy
6.6 Shift Im, ariant Sets
6.7 Construction of Shift Invariant Sets
6.8 Snap-back Repeller as a Shift Invariant Set
Notes for Chapter 6
7 The Smale Horseshoe
7.1 The Standard Smale Horseshoe
7.2 The General Horseshoe
Notes for Chapter 7
8 Fractals
8.1 Examples of Fractals
8.2 HausdorffDimension and the HausdorffMeasure
8.3 Iterated Function Systems (IFS)
Notes fbr Chapter 8
9 Rapid Fluctuations of Chaotic Maps on RN
9.1 Total Variation for Vector-Value Maps
9.2 Rapid Fluctuations of Maps on ]RN
9.3 Rapid Fluctuations of Systems with Quasi-shift Invariant Sets
9.4 Rapid Fluctuations of Systems Containing Topological Horseshoes
9.5 Examples of Applications of Rapid Fluctuatkms
Notes for Chapter 9
10 Infinite-dimensional Systems Induced by Continuous-Time Difference Equations
10.1 I3DS
10.2 Rates of Growth of Total Varkations of Iterates
1 Simple Interval Maps and Their Iterations
1.1 Introduction
1.2 The Inverse and hnplicit Function Theorems
1.3 Visualizing from the Graphics oflterations of the Quadratic Map
Notes for Chapter 1
2 Total Variations of Iterates of Maps
2.1 The Use of Total Variations as a Measure of Chaos
Notes for Chapter 2
3 Ordering among Periods: The Sharkovski Theorem
Notes for Chapter 3
4 Bifurcation Theorems for Maps
4.1 The Period-Doubling Bifurcation Theorem
4.2 Saddle-Node Bifurcations
4.3 The Pitchfork Bifurcation
4.4 Hopf Bifurcation
Notes for Chapter 4
5 Homoclinicity. LyapunoffExponents
5.1 Homoclinic Orbits
5.2 Lyapunoff Exponents
Notes for Chapter 5
6 Symbolic Dynamics, Conjugacy and Shift Invariant Sets
6.1 The Itinerary of an Orbit
6.2 Properties of the shift map σ
6.3 Symbolic Dynamical Systems Σk and Σk+
6.4 The Dynamics of (Σl+，σ+) and Chaos
6.5 Topological Conjugacy and Semiconjugacy
6.6 Shift Im, ariant Sets
6.7 Construction of Shift Invariant Sets
6.8 Snap-back Repeller as a Shift Invariant Set
Notes for Chapter 6
7 The Smale Horseshoe
7.1 The Standard Smale Horseshoe
7.2 The General Horseshoe
Notes for Chapter 7
8 Fractals
8.1 Examples of Fractals
8.2 HausdorffDimension and the HausdorffMeasure
8.3 Iterated Function Systems (IFS)
Notes fbr Chapter 8
9 Rapid Fluctuations of Chaotic Maps on RN
9.1 Total Variation for Vector-Value Maps
9.2 Rapid Fluctuations of Maps on ]RN
9.3 Rapid Fluctuations of Systems with Quasi-shift Invariant Sets
9.4 Rapid Fluctuations of Systems Containing Topological Horseshoes
9.5 Examples of Applications of Rapid Fluctuatkms
Notes for Chapter 9
10 Infinite-dimensional Systems Induced by Continuous-Time Difference Equations
10.1 I3DS
10.2 Rates of Growth of Total Varkations of Iterates
