The Chaos Avant-garde: Memories of the Early Days of Chaos Theory (Google eBook)

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World Scientific, Jan 1, 2001 - Chaotic behavior in systems - 231 pages
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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 OCo 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 1959OCo1962 (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 OC PrehistoricOCO 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 RAssler). Readership: Educators and university students of science and mathematics."

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Finding a Horseshoe on the Beaches of Rio
Strange Attractors and the Origin of Chaos
My Encounter with Chaos
Reflections on the Origin of the BrokenEgg Chaotic Attractor
A Personal View
The Butterfly Effect
The Turbulence Paper of D Ruelle and F Takens
Exploring Chaos on an Interval

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Page 5 - ... the only go player in the Soviet Union. My roommate in Kiev was Larry Markus. I met and saw much of Anosov in Kiev. Anosov had followed the Gorki school, but he was based in Moscow. After Kiev I went back to Moscow where Anosov introduced me to Arnold, Novikov, and Sinai. I must say I was extraordinarily impressed to meet such a powerful group of four young mathematicians. In the following years, I often said there was nothing like that in the West. I gave some lectures at the Steklov Institute...
Page 3 - Morse inequalities for a class of dynamical systems incorporating it. However, my overenthusiasm led me to suggest in the paper that these systems were almost all (an open dense set) of ordinary differential equations! If I had been at all familiar with the literature (Poincaré, Birkhoff, Cartwright-Littlewood), I would have seen how crazy this idea was. On the other hand, these systems, though sharply limited, would find a place in the literature, and were christened Morse-Smale dynamical systems...

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About the author (2001)

Ralph Abraham is the author of "Dynamics: The Geometry of Behavior". He lives in California.

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