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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