98-7 N. Chernov, R. Markarian, S. Troubetzkoy

Invariant measures for Anosov maps with small holes (124K, LATeX) Jan 6, 98

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Abstract. We study Anosov diffeomorphisms on surfaces with small holes. The points that are mapped into the holes disappear and never return. In our previous paper, we proved the existence of a conditionally invariant measure $\mu_+$. Here we show that the iterations of any initially smooth measure, after renormalization, converge to $\mu_+$. We construct the related invariant measure on the repeller and prove that it is ergodic and K-mixing. We prove the escape rate formula, relating the escape rate to the positive Lyapunov exponent and the entropy.

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