《非線性物理科學(xué)：離散和切換動力系統(tǒng)（英文版）》特色： ● 首次給出離散動力系統(tǒng)的穩(wěn)定性和分叉的詳盡分類 ● 介紹離散動力系統(tǒng)具有高階奇異性的穩(wěn)定性和分叉理論 ● 討論非線性離散系統(tǒng)的不動點(diǎn)和混沌的陰陽解 ● 分析在離散系統(tǒng)中混沌分形性和物理系統(tǒng)映射的構(gòu)造 ● 研究不連續(xù)系統(tǒng)中的映射動力學(xué)，擦邊不變形及奇異吸引子碎裂 ● 讀者群大，應(yīng)用面廣 ● 直觀、簡潔、易讀
Preface
Chapter 1 Linear Discrete Systems and Stability
1.1 Basic iterative solutions
1.2 Linear discrete systems with distinct eigenvalues
1.3 Linear discrete systems with repeated eigenvalues
1.4 Stability and boundary
1.5 Lower-dimensional discrete systems
1.5.1 One-dimensional systems
1.5.2 Planar discrete linear systems
1.5.3 Three-dimensional discrete systems
Reference
Chapter 2 Stability, Bifurcation and Routes to Chaos
2.1 Discrete dynamical systems
2.2 Fixed points and stability
2.3 Bifurcation and stability switching
Preface
Chapter 1 Linear Discrete Systems and Stability
1.1 Basic iterative solutions
1.2 Linear discrete systems with distinct eigenvalues
1.3 Linear discrete systems with repeated eigenvalues
1.4 Stability and boundary
1.5 Lower-dimensional discrete systems
1.5.1 One-dimensional systems
1.5.2 Planar discrete linear systems
1.5.3 Three-dimensional discrete systems
Reference
Chapter 2 Stability, Bifurcation and Routes to Chaos
2.1 Discrete dynamical systems
2.2 Fixed points and stability
2.3 Bifurcation and stability switching
2.3.1 Stability and switching
2.3.2 Bifurcations
2.4 Routes to chaos
2.4.1 One-dimensional maps
2.4.2 Two-dimensional maps
References
Chapter 3 Fractality and Complete Dynamics
3.1 Multifractals in 1-D iterative maps
3.1.1 Similar structures in period doubling
3.1.2 Fractality of chaos via period doubling bifurcations
3.1.3 An example
3.2 Bouncing ball dynamics
3.2.1 Periodic motions
3.2.2 Stability and bifurcations
3.2.3 Numerical illustrations
3.3 Positive and negative dynamics of discrete systems
3.4 Complete dynamics of Henon map
References
Chapter 4 Switching Systems with Transports
4.1 Continuous subsystems
4.2 Switching systems
4.3 Measuring functions and stability
4.4 Mappings and periodic flows
4.5 Linear switching systems
4.5.1 Vibrations with piecewise forces
4.5.2 Vector fields switching
References
Chapter 5 Mapping Dynamics and Fragmentation
5.1 Discontinuous dynamical systems
5.2 G-functions to boundaries
5.3 Mapping dynamics
5.4 A semi-active suspension system
5.4.1 Analytical dynamics
5.4.2 Illustrations
5.5 Grazing singular sets and fragmentation
5.6 Fragmentized strange attractors
References
Index
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