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Dynamical systems with generalized hyperbolic attractors: hyperbolic, ergodic and topological properties

Published online by Cambridge University Press:  19 September 2008

Ya. B. Pesin
Ya. B. Pesin
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA.
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Abstract

We introduce a class of dynamical systems on a Riemannian manifold with singularities having attractors with strong hyperbolic behavior of trajectories. This class includes a number of famous examples such as the Lorenz type attractor, the Lozi attractor and some others which have been of great interest in recent years. We prove the existence of a special invariant measure which is an analog of the Bowen-Ruelle-Sinai measure for classical hyperbolic attractors and study the ergodic properties of the system with respect to this measure. We also describe some topological properties of the system on the attractor. Our results can be considered a dissipative version of the theory of systems with singularities preserving the smooth measure.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 1 , March 1992 , pp. 123 - 151
Copyright
Copyright © Cambridge University Press 1992

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