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The Topology of Chaos. Alice in Stretch and Squeezeland. 2nd Edition

  • ID: 2245486
  • Book
  • November 2011
  • 618 Pages
  • John Wiley and Sons Ltd
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The 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
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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


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On the first edition

"A short review can only hint at the wealth of ideas here...highly recommended." (Choice, Vol. 40, No. 7, March 2003)

"In this third book Gilmore and Lefranc step one more rung up the ladder of dynamical complexity..." (American Journal of Physics, Vol. 71, No. 5, May 2003)

"This authoritative monograph advances innovative methods for the analysis of chaotic systems." (Journal of Mathematical Psychology, Vol. 47, 2003)
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