附註:Includes bibliographical references.
Preface; Contents; 1. On How I Got Started in Dynamical Systems 1959-1962; 2. Finding a Horseshoe on the Beaches of Rio; What is Chaos?; Taxpayers Money; Flying Down to Rio; Mathematics on the Beach; Letter from America; The Horseshoe; The Horseshoe and Chaos: Coin Flipping; The Hidden Origins of Chaos; The Third Force; Good Luck; 3. Strange Attractors and the Origin of Chaos; Prologue; The Oldest Chaos in a Non-Autonomous System- A Shattered Egg; Encounter with the Japanese Attractor; The Hayashi Laboratory at the Time of the ""McGraw-Hill Book""
From the Harmonic Balance Method to the Mapping MethodThe True Value of an Advisor: A Scion of Chaos; The End of the Chihiro Hayashi Laboratory; The Original Data that were Preserved; Epilogue; References; Acknowledgments; 4. My Encounter with Chaos; By the Time It's Popular It's Too Late; The Oldest Attractor was a Result of Perseverance Not of Wisdom; Professor's Principles and Mutual Trust; Publication of My First ""Chaos"" Paper; Since Chaos Became Fashionable; 5. Reflections on the Origin of the Broken-Egg Chaotic Attractor; Introduction; The broken-egg chaotic attractors
Modified Rayleigh/Duffing/Van der Pol equationsProposal of a periodically forced two-dimensional system; Numerical experiments based on perturbation theory; Conclusion; Acknowledgments; References; 6. The Chaos Revolution: A Personal View; Introduction; The Discovery of the Homoclinic Tangle by Poincare 1889; From Paris to Mexico City: The First 70 Years of Chaos Theory; The Golden Years of Global Analysis: Berkeley 1960-1968; The Chaos Revolution: 1968-1998; Conclusion; Bibliography; 7. The Butterfly Effect
Predictability: Does the Flap of a Butterfly's Wings in Brazil Set off a Tornado in Texas?8. I. Gumowski and a Toulouse Research Group in the ""Prehistoric"" Times of Chaotic Dynamics; 1. Introduction. Birth of the group. Approach of dynamic problems (processes).; 2. First Contact with Complex Dynamics (1958-1960); 3. Basin Boundaries of Two-Dimensional Noninvertible Maps (1963-1975); 4. Chaotic Attractors of Two-Dimensional Noninvertible Maps (1968-1975); 5. Normal Forms for Resonant Bifurcations (1969-1974); 6. Two-Dimensional Conservative Maps (1970-1975)
7. Study of One-Dimensional Non-invertible Maps (from 1972)8. Applications; 9. The International Colloquium "" Transformations Ponctuelles et leurs Applications"" (Point mapping and Applications): Two Exhibitions of Chaotic Images (1973 and 1975); 10. Conclusion; References; 9. The Turbulence Paper of D. Ruelle and F. Takens; 10. Exploring Chaos on an Interval; References; 11. Chaos Hyperchaos and the Double-Perspective; Chaos and Hyperchaos; Superfat Attractors; Owls and Cats; The Interface; Acknowledgments; References; Sources
摘要:This book is an authoritative and unique reference for the history of chaos theory, told by the pioneers themselves. It also provides an excellent historical introduction to the concepts. There are eleven contributions, and six of them are published here for the first time - two by Steve Smale, three by Yoshisuke Ueda, and one each by Ralph Abraham, Edward Lorenz, Christian Mira, Floris Takens, T Y Li and James A Yorke, and Otto E Rossler. Contents: On How I Got Started in Dynamical Systems 1959-1962 (S Smale); Finding a Horseshoe on the Beaches of Rio (S Smale); Strange Attractors and the Ori.
