N. Chernov, R. Markarian, S. Troubetzkoy
Invariant measures for Anosov maps with small holes
(124K, LATeX)

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.