Ergodic Theory and Dynamical Systems

Research Article

Escape rates for Gibbs measures

ANDREW FERGUSONa1 and MARK POLLICOTTa1

a1 Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK (email: a.j.ferguson@warwick.ac.uk, m.pollicott@warwick.ac.uk)

Abstract

In this paper we study the asymptotic behaviour of the escape rate of a Gibbs measure supported on a conformal repeller through a small hole. There are additional applications to the convergence of the Hausdorff dimension of the survivor set.

(Received August 30 2010)

(Revised January 04 2011)

(Online publication April 27 2011)