Chaos in Discrete Dynamical Systems: A Visual Introduction in 2 Dimensions

Chaos in Discrete Dynamical Systems: A Visual Introduction in 2 Dimensions

Paperback(Softcover reprint of the original 1st ed. 1997)

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Overview

The materials in the book and on the accompanying disc are not solely developed with only the researcher and professional in mind, but also with consideration for the student: most of this material has been class-tested by the authors. The book is packed with some 100 computer graphics to illustrate the material, and the CD-ROM contains full-colour animations tied directly to the subject matter of the book itself. The cross-platform CD also contains the program ENDO, which enables users to create their own 2-D imagery with X-Windows. Maple scripts are provided to allow readers to work directly with the code from which the graphics in the book were taken.

Product Details

ISBN-13: 9781461273479
Publisher: Springer New York
Publication date: 04/19/2013
Edition description: Softcover reprint of the original 1st ed. 1997
Pages: 246
Product dimensions: 6.69(w) x 9.61(h) x (d)

Table of Contents

of the Book.- 1 Introduction.- 2 Basic concepts in 1D.- 3 Basic concepts in 2D.- 4 Absorbing Areas.- 5 Holes.- 6 Fractal Boundaries.- 7 Chaotic Contact Bifurcations.- 8 Conclusion.- Appendix 1 Notations.- A1.1 Formal logic.- A1.2 Set theory.- A1.3 Point set topology.- Appendix 2 Topological Dynamics.- A2.1 Trajectories and orbits.- A2.2 Inverse images.- A2.3 Fixed points.- A2.4 Periodic trajectories.- A2.5 Limit points.- A2.6 Stable sets, attractors, and basins.- A2.7 Unstable sets and repellors.- A2.8 Chaotic attractors.- Appendix 3 Critical Curves.- A3.1 The zones.- A3.2 Critical points via calculus.- A3.3 Critical points via topology.- A3.4 The critical curves.- A3.5 Absorbing areas.- Appendix 4 Synonyms.- Appendix 5 History, Part 1.- A5.1 Early history.- A5.2 Finite difference equations.- A5.3 Functional equations.- A5.4 Poincaré.- A5.5 Independent contemporaries of Poincaré.- A5.6 Birkhoff.- A5.7 Denjoy.- A5.8 The Russian school.- A5.9 The Japanese school.- A5.10 Conservative systems.- A5.11 The American school.- A5.12 Numerical methods and applied work.- A5.13 Iteration theory.- A5.14 The methods of Liapunov.- A5.15 Periodic solutions.- A5.16 Control theory.- A5.17 Other applications.- A5.18 Conclusion.- A5.19 Historical Bibliography.- Appendix 6 History, Part 2.- A6.1 Introduction.- A6.2 G.D. Birkhoff.- A6.3 Nonlinear oscillations from 1925.- A6.4 The Mandelstham-Andronov school.- A6.5 The Bogoliubov (or Kiev) school.- A6.6 Poincaré’s analyticity theorem.- A6.7 Myrberg’s contribution.- A6.8 Conclusion.- Appendix 7 Domains of the Figures.- Frequently used references by code.- Bibliography by author.

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