Contents
Acknowledgment ix
Chapter 1. Introduction 1
Chapter 2. Discrete Dynamical Systems 8
2.1. Limit sets 8
2.2. Stability of invariant sets and asymptotically smooth maps 10
2.3. Examples of asymptotically smooth maps 13
2.4. Dissipativeness and global attractors 16
2.5. Dependence on parameters 21
2.6. Fixed point theorems 23
2.7. Stability relative to the global attractor and Morse-Smale maps 25
2.8. Dimension of the global attractor 26
2.9. Dissipativeness in two spaces 28
Notes and Remarks 33
Chapter 3. Continuous Dynamical Systems 35
3.1. Limit sets 35
3.2. Asymptotically smooth and ^-contracting semigroups 36
3.3. Stability of invariant sets 38
3.4. Dissipativeness and global attractors 38
3.5. Dependence on parameters 40
3.6. Periodic processes 41
3.7. Skew product flows 43
3.8. Gradient flows 49
3.9. Dissipativeness in two spaces 54
3.10. Properties of the flow on the global attractor 56
Notes and Remarks 60
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