The Chaos Avant-garde: Memories of the Early Days of Chaos TheoryThis 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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Chaos Avant-garde, The: Memoirs Of The Early Days Of Chaos Theory Ralph Abraham,Yoshisuke Ueda Pré-visualização limitada - 2001 |
The Chaos Avant-garde: Memories of the Early Days of Chaos Theory Ralph Abraham,Yoshisuke Ueda Pré-visualização limitada - 2000 |
Palavras e frases frequentes
Acad amplitude analog computer appear Applications attractor basin basin boundary behavior bifurcation called chaos chaotic chaotic attractor closed complex conservative considered continuous corresponding critical curve cycles defined described differential equations domain doubling dynamical systems engineering example existence experiments Figure fixed point force fractal frequency give given Gumowski harmonic Hayashi homoclinic points horseshoe ideas important increases Institute interest International introduced invariant laboratory leads limit manifolds Math mathematicians mathematics mechanics method Mira motion nonlinear Nonlinear Oscillations Note observed obtained occurs original oscillation parameter Paris particular period phase phenomena physics plane Poincaré present problem Prof Professor properties publication published quantum mechanics region represented saddle Sciences sequence simulation situation Smale solutions stable structure studies term theory topology transformations Ueda University unstable values York
Passagens conhecidas
Página 91 - If the flap of a butterfly's wings can be instrumental in generating a tornado, it can equally well be instrumental in preventing a tornado.
Página 20 - One will be struck by the complexity of this figure, which I am not even going to attempt to draw. Nothing can better give us an idea of the difficulty of the three-body problem, and of dynamics problems in general...
Página 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...
Página 197 - Sur les formes réduites des transformations ponctuelles dans le domaine d'un point double.
Página 44 - Akamatsu (seven years my junior) came into the master's program. Another Tokushima native, he chose nonlinear oscillation as the subject of his research from the very start and came directly under my guidance. I asked him to begin with the application of the mapping method to the research in synchronization phenomenon, for which the harmonic balance method had been the standard method in the past. A part of his master's thesis is described in the latter half of reference [9]. These two students from...
Página 32 - Co. [4]) accepted the challenge, knowing it was a difficult job. Even if I did not want to do it, I would not have been able to refuse him anyway. I was a little amused to find this most exalted professor high up in the clouds a bit flustered, especially with the objection written in English, no less! As it was impossible to solve the...
Página 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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Informação bibliográfica
| Título | The Chaos Avant-garde: Memories of the Early Days of Chaos Theory Volume 39 de World Scientific series on nonlinear science: Monographs and treatises |
| Autores | Ralph Abraham, Yoshisuke Ueda |
| Editora | World Scientific, 2000 |
| ISBN | 9812386475, 9789812386472 |
| Número de páginas | 221 páginas |
| Exportar citação | BiBTeX EndNote RefMan |