Ergodic Theory and Dynamical Systems

Research Article

Hausdorff dimension for horseshoes

Heather McCluskeya1 and Anthony Manninga1

a1 Mathematics Institute, University of Warwick, Coventry CV4 7AL, England

Abstract

We shall measure how thick a basic set of a C1 axiom A diffeomorphism of a surface is by the Hausdorff dimension of its intersection with an unstable manifold. This depends continuously on the diffeomorphism. Generically a C2 diffeomorphism has attractors whose Hausdorff dimension is not approximated by the dimension of its ergodic measures.

(Received October 20 1982)