Communications in Mathematical Physics

, Volume 218, Issue 1, pp 1–97

Strange Attractors with One Direction of Instability

  • Qiudong Wang
  • Lai-Sang Young

DOI: 10.1007/s002200100379

Cite this article as:
Wang, Q. & Young, L. Commun. Math. Phys. (2001) 218: 1. doi:10.1007/s002200100379

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Qiudong Wang
    • 1
  • Lai-Sang Young
    • 2
  1. 1.Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA.¶E-mail: dwang@math.arizona.eduUS
  2. 2.Courant Institute of Mathematical Sciences, 251 Mercer St., New York, NY 10012, USA.¶E-mail:lsy@cims.nyu.eduUS
  3. 3.Department of Mathematics, UCLA, Los Angeles, CA 90095, USA. E-mail: lsy@math.ucla.eduUS