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1 online resource (231 pages) |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
World Scientific Series On Nonlinear Science Series A ; v.39 |
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World Scientific Series On Nonlinear Science Series A
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| Note |
Intro -- Contents -- Preface -- 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 Method -- The 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 equations -- Proposal 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? |
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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 |
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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 Origin of Chaos (Y Ueda); My Encounter with Chaos (Y Ueda); Reflections on the Origin of the Broken-Egg Chaotic Attractor (Y Ueda); The Chaos Revolution: A Personal View (R Abraham); The Butterfly Effect (E Lorenz); I Gumowski and a Toulouse Research Group in the "Prehistoric" Times of Chaotic Dynamics (C Mira); The Turbulence Paper of D Ruelle & F Takens (F Takens); Exploring Chaos on an Interval (T Y Li & J A Yorke); Chaos, Hyperchaos and the Double-Perspective (O E Rössler). Readership: Educators and university students of science and mathematics |
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Description based on publisher supplied metadata and other sources |
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries |
| Link |
Print version: Abraham, Ralph Chaos Avant-garde, The: Memoirs Of The Early Days Of Chaos Theory
Singapore : World Scientific Publishing Company,c2000 9789810244040
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| Subject |
Chaotic behavior in systems -- Research -- History.;Mathematics -- Research -- History
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Electronic books
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| Alt Author |
Ueda, Yoshisuke
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