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New Developments in Dynamics: Hyperbolicity and Chaotic Dynamics

Published online by Cambridge University Press:  07 August 2017

J. Palis
J. Palis*
Affiliation:
Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jd. Botânico, 22.460 - Rio de Janeiro, Brazil

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Two important theories in Dynamical Systems were constructed in the sixties: the hyperbolic theory for general systems and the KAM (after Kolmogorov, Arnold and Moser) theory for conservative systems as the ones that appear in Celestial Mechanics. Most of our discussions here concern dissipative (or locally dissipative) systems, although most questions are now being posed for area preserving maps (symplectic maps in higher dimensions). Moreover, one can argue that understanding dynamically small dissipative perturbations of conservative systems is of much importance: indeed it has been recently shown that a KAM curve (tori in higher dimension) can be destroyed and in fact engulfed in the basin of attraction of a Hénon-like strange attractor as defined below.

Type
Part VII - Dynamical Systems. Maps. Integrators
Information
Symposium - International Astronomical Union , Volume 152: Chaos, Resonance and Collective Dynamical Phenomena in the Solar System , 1992 , pp. 363 - 368
Copyright
Copyright © Kluwer 1992 

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