CONTENTS OF THE BOOK

Front matter
• Foreword to the Project
• Preface to the Book
• About the Book Authors
• Preface to the CD-ROM
• About the CD-ROM Authors
• Preface to the Website
• Acknowledgments

PART BASIC CONCEPTS

• Chapter 1, Introduction, 3
  • 1.1 Background, 3
  • 1.2 History, 3
  • 1.3 Plan of the book, 4
  • 1.4 Context, 5
  • 1.5 Basic concepts of iteration theory, 6
  • 1.6 The families of maps, 8
  • 1.7 Critical points and curves, 9

• Chapter 2, Basic concepts in 1D, 11
  • 2.1 Maps, 11
  • 2.2 Multiplicities, 12
  • 2.3 Trajectories and orbits, 14
  • 2.4 Attractors, basins, and boundaries, 22
  • 2.5 Bifurcations, 23
  • 2.6 Exemplary bifurcations, 24

• Chapter 3, Basic concepts in 2D, 29
  • 3.1 Maps, 29
  • 3.2 Multiplicities and critical curves, 30
  • 3.3 An example, 30
  • 3.4 Trajectories and orbits, 36
  • 3.5 Attractors, 36
  • 3.6 Bifurcations, 37

PART 2, EXEMPLARY BIFURCATION SEQUENCES, 39

• Chapter 4, Absorbing Areas, 41
  • 4.1 Absorption concepts, 1D, 41
  • 4.2 Absorption concepts, 2D, 41
  • 4.3 Exemplary bifurcation sequence, 44
• Chapter 5Holes, 61
  • 5.1 Introduction, 61
  • 5.2 Exemplary bifurcation sequence, 61
• Chapter 6Fractal Boundaries, 89
  • 6.1 Contact bifurcation concepts, 89
  • 6.2 Exemplary bifurcation sequence, 103
• Chapter 7Chaotic Contact Bifurcations, 123
  • 7.1 Bifurcations in one dimension, 123
  • 7.2 Bifurcations in two dimensions, 141
  • 7.3 Exemplary bifurcation sequence, 145
• Chapter 8, Conclusion, 165

PART 3, APPENDICES, 167

• Appendix 1Notations, 169
  • A1.1 Formal logic 169
  • A1.2 Set theory 169
• Appendix 2Topological Dynamics, 171
  • A2.1 Trajectories and orbits , 171
  • A2.2 Inverse images 172
  • A2.3 Fixed points 172
  • A2.4 Periodic trajectories 173
  • A2.5 Limit points 173
  • A2.6 Stable sets, attractors, and basins 173
  • A2.7 Unstable sets and repellors 174
  • A2.8 Chaotic attractors 175
• Appendix 3Critical Curves177
  • A3.1 The zones 177
  • A3.2 Critical points via calculus 178
  • A3.3 Critical points via topology 179
  • A3.4 The critical curves 180
  • A3.5 Absorbing areas 180
• Appendix 4Synonyms181
• Appendix 5History, Part 1183
  • A5.1 Early history183
  • A5.2 Finite difference equations184
  • A5.3 Functional equations185
  • A5.4 Poincar]186
  • A5.5 Independent contemporaries of Poincar]188
  • A5.6 Birkhoff189
  • A5.7 Denjoy190
  • A5.8 The Russian school190
  • A5.9 The Japanese school192
  • A5.10 Conservative systems192
  • A5.11 The American school194
  • A5.12 Numerical methods and applied work194
  • A5.13 Iteration theory195
  • A5.14 The methods of Liapunov196
  • A5.15 Periodic solutions196
  • A5.16 Control theory197
  • A5.17 Other applications197
  • A5.18 Conclusion198
  • A5.19 Historical Bibliography198
• Appendix 6History, Part 2225
  • A6.1 Introduction225
  • A6.2 G.D. Birkhoff227
  • A6.3 Nonlinear oscillations from 1925230
  • A6.4 The Mandelstham-Andronov school232
  • A6.5 The Bogoliubov (or Kiev) school241
  • A6.6 Poincare's analyticity theorem242
  • A6.7 Myrberg's contribution243
  • A6.8 Conclusion246
• Appendix 7, Domains for the Figures, 249
• Bibliography255
• Index265