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

ISBN-13: 9781461273479 / Angielski / Miękka / 2013 / 246 str.

Ralph Abraham; Laura Gardini; Christian Mira

Opis

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.

Spis treści

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.

O autorze

Chaos and Discrete Dynamical Systems is a unique, first-of-its-kind book/CD-ROM package which contains information relating to chaos, bifurcations and critical curves in 2-dimensions. It is of interest to a wide range of scientists, engineers and students in mathematics, engineering, physics, and other interested in and involved with complex dynamical systems.