N. Chernov and R. Markarian
Ergodic properties of Anosov maps with rectangular holes
(96K, LATeX)

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.