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.
Article PDF
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 25 April 2000 / Accepted: 17 October 2000
Rights and permissions
About this article
Cite this article
Wang, Q., Young, LS. Strange Attractors with One Direction of Instability. Commun. Math. Phys. 218, 1–97 (2001). https://doi.org/10.1007/s002200100379
Issue Date:
DOI: https://doi.org/10.1007/s002200100379