97-264 N. Chernov and R. Markarian

Ergodic properties of Anosov maps with rectangular holes (96K, LATeX) May 13, 97

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Abstract. We study Anosov diffeomorphisms on manifolds in which some `holes' are cut. The points that are mapped into those holes disappear and never return. The holes studied here are rectangles of a Markov partition. Such maps generalize Smale's horseshoes and certain open billiards. The set of nonwandering points of a map of this kind is a Cantor-like set called a repeller. We construct invariant and conditionally invariant measures on the sets of nonwandering points. Then we establish ergodic, statistical, and fractal properties of those measures.

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