Ergodic Theory and Dynamical Systems

Research Article

Entropy and semi-conjugacy in dimension two

Michael Handela1

a1 Department of Mathematics and Computer Science, Lehman College, Bronx, New York 10468, USA

Abstract

We prove that if a diffeomorphism f of a closed surface is homotopic to and has the same topological entropy as a pseudo-Anosov homeomorphism g, then f is semi-conjugate to g. As part of the proof, a necessary and sufficient condition is given for a pseudo-orbit of a pseudo-Anosov homeomorphism g to be shadowed by an actual orbit of g.

(Received May 18 1987)

(Revised December 03 1987)