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.