To appear in Ergodic Theory and Dynamical Systems. PRODUCT STRUCTURE OF POINCARÉ RECURRENCE
نویسنده
چکیده
We provide new non-trivial quantitative information on the behavior of Poincaré recurrence. In particular we establish the almost everywhere coincidence of the recurrence rate and of the pointwise dimension for a large class of repellers, including repellers without finite Markov partitions. Using this information, we are able to show that for locally maximal hyperbolic sets the recurrence rate possesses a certain local product structure, which closely imitates the product structure provided by the families of local stable and unstable manifolds, as well as the almost product structure of hyperbolic measures.
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