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

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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.

Original languageEnglish (US)
Pages (from-to)123-151
Number of pages29
JournalErgodic Theory and Dynamical Systems
Volume12
Issue number1
DOIs
StatePublished - Mar 1992

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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