Showing papers by "Lai Sang Young published in 2001"
TL;DR: In this article, the existence of attractors with a single direction of instability and certain controlled behaviors was shown to exist for strongly dissipative maps with d = 2 phase-dimensions.
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.
202 citations