Strange Attractors with One Direction of Instability |
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Authors: | Qiudong Wang Lai-Sang Young |
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Institution: | Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA.?E-mail: dwang@math.arizona.edu, US Courant Institute of Mathematical Sciences, 251 Mercer St., New York, NY 10012, USA.?E-mail:lsy@cims.nyu.edu, US
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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.
Received: 25 April 2000 / Accepted: 17 October 2000 |
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