Chaos in Discrete Dynamical Systems

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.