- 98-7 N. Chernov, R. Markarian, S. Troubetzkoy
- Invariant measures for Anosov maps with small holes
Jan 6, 98
(auto. generated ps),
of related papers
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.