Smooth Dynamical Systems
Published on 12. August 1980
258 pages
978-0-08-087410-4 (ISBN)
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Smooth Dynamical Systems
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M. C. Irwin
Smooth Dynamical Systems
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07/1997
Academic Press
€97.80
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Content
- Front Cover
- Smooth Dynamical Systems
- Copyright Page
- Contents
- Preface
- Introduction
- I. The simple pendulum
- II. A dissipative system
- III. The spherical pendulum
- IV. Vector fields and dynamical systems
- Chapter 1. Some Simple Examples
- I. Flows and homeomorphisms
- II. Orbits
- III. Examples of dynamical systems
- IV. Constructing systems
- V. Properties of orbits
- Appendix 1
- Chapter 2. Equivalent Systems
- I. Topological conjugacy
- II. Homeomorphisms of the circle
- III. Flow equivalence and topological equivalence
- IV. Local equivalence
- V. Limit sets of flows
- VI. Limit sets of homeomorphisms
- VII. Non-wandering sets
- Appendix 2
- Chapter 3. Integration of Vector Fields
- I. Vector fields
- II. Velocity vector fields and integral flows
- III. Ordinary differential equations
- IV. Local integrals
- V. Global integrals
- Appendix 3
- Chapter 4. Linear Systems
- I. Linear flows on Rn
- II. Linear automorphisms of Rn
- III. The spectrum of a linear endomorphism .
- IV. Hyperbolic linear automorphisms
- V. Hyperbolic linear vector fields
- Appendix 4
- Chapter 5. Linearization
- I. Regular points
- II. Hartman's theorem
- III. Hartman's theorem for flows
- IV. Hyperbolic closed orbits
- Appendix 5
- Chapter 6. Stable Manifolds
- I. The stable manifold at a hyperbolic fixed point of a diffeomorphism
- II. Stable manifold theory for flows
- III. The generalized stable manifold theorem
- Appendix 6
- Chapter 7. Stable Systems
- I. Low dimensional systems
- II. Anosov systems
- III. Characterization of structural stability
- IV. Density
- V. Omega stability
- VI. Bifurcation
- Appendix A. Theory of Manifolds
- Appendix B. Map Spaces
- Appendix C. The Contraction Mapping Theorem
- Bibliography
- Subject Index
