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Introduction to Dynamical Systems, An
ISBN-10: 0-13-143140-4
ISBN-13: 978-0-13-143140-9
Published by Addison-Wesley
© 2004
Pub. Date: Jan 5, 2004
Format: Paper
Table of Contents
(NOTE: Each chapter concludes with Applications, Theory and Proofs, and Exercises.)
Prologue: Historical Perspective.
Prologue: Historical Perspective.
I. SYSTEMS OF DIFFERENTIAL EQUATIONS.
1. Geometric Approach to Differential Equations.
2. Linear Systems.
3. The Flow: Solutions of Nonlinear Equations.
4. Phase Portraits with Emphasis on Fixed Points.
5. Phase Portraits Using Energy and Other Test Functions.
6. Periodic Orbits.
7. Chaotic Attractors.
II. ITERATION OF FUNCTIONS.
8. Iteration of Functions as Dynamics.
9. Periodic Points of One-Dimensional Maps.
10. Itineraries for One-Dimensional Maps.
11. Invariant Sets for One-Dimensional Maps.
12. Periodic Points of Higher Dimensional Maps.
13. Invariant Sets for Higher Dimensional Maps.
14. Fractals.
Appendix A: Calculus Background.
Appendix B: Analysis and Topology Terminology.
Appendix C: Linear Algebra Background.
Bibliography.
Index.
