Strange attractors with one direction of instability

Qiudong Wang, Lai-Sang Young

Research output: Contribution to journalArticle

Abstract

We give simple conditions that guarantee, for strongly dissipative maps, the existence of strange attractors with a single direction of instability and certain controlled behaviors. Only the d = 2 case is treated in this paper, although our approach is by no means limited to two phase-dimensions. We develop a dynamical picture for the attractors in this class, proving they have many of the statistical properties associated with chaos: positive Lyapunov exponents, existence of SRB measures, and exponential decay of correlations. Other results include the geometry of fractal critical sets, nonuniform hyperbolic behavior, symbolic coding of orbits, and formulas for topological entropy.

Original languageEnglish (US)
Pages (from-to)1-97
Number of pages97
JournalCommunications in Mathematical Physics
Volume218
Issue number1
DOIs
Publication statusPublished - Apr 2001

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ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

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