- Language: English
- 390 Pages
- Published: December 2011
The Topology of Chaos. Alice in Stretch and Squeezeland. 2nd Edition
- Published: November 2011
- 618 Pages
- John Wiley and Sons Ltd
T he Topology of Chaos is a highly valued resource for those who wish to move from an introductory knowledge of chaotic behavior to a more sophisticated and precise understanding of chaotic systems and measurements made on them. The authors provide deep insight into the structure of strange attractors, how they are classified, and how the information required to characterize a strange attractor can be extracted from experimental data. What makes this book special is the abundance of practical examples where time series from real physical systems (e.g. lasers) are analyzed using topological techniques. Hence it has become the experimenter’s guidebook to reliable studies of experimental data for comparison with candidate theoretical models, invaluable to physicists, mathematicians, and engineers studying low–dimensional chaotic systems. This second edition incorporates recent advances in the field, such as the concept of bounding tori. From the contents: Discrete Dynamical Systems: Maps Continuous Dynamical Systems: Flows Topological Invariants Branched Manifolds Topological Analysis Program Folding Mechanisms: A2 Tearing Mechanisms: A3 Unfoldings Symmetry Bounding Tori Representation Theory for Strange Attractors Flows in Higher Dimensions Program for Dynamical System Theory
Preface 1. Introduction 2. Discrete Dynamical Systems: Maps 3. Continuous Dynamical Systems: Flows 4. Topological Invariants 5. Branched Manifolds 6. Topological Analysis Program 7. Folding Mechanisms: A2 8. Tearing Mechanisms: A3 9. Unfoldings 10. Symmetry 11. Bounding Tori 12. Representation Theory for Strange Attractors 13. Flows in Higher Dimensions 14. Program for Dynamical System Theory Appendix A: Determining Templates from Topological Invariants Appendix B: Embeddings References
Robert Gilmore Drexel University, US.
Marc Lefranc University of Lille, France.