Higher-dimensional subshifts of finite type, factor maps and measures of maximal entropy

Ronald Meester and Jeffrey E. Steif

Vol. 200 (2001), No. 2, 497–510

DOI: 10.2140/pjm.2001.200.497

Abstract

We investigate factor maps of higher-dimensional subshifts of finite type. In particular, we are interested in how the number of ergodic measures of maximal entropy behaves under such factor maps. We show that this number is preserved under almost invertible maps, but not in general under finite to one factor maps. One of our tools, which is of independent interest, is a higher-dimensional characterization of entropy-preserving factor maps that extends the well-known one-dimensional characterization result.

Milestones

Received: 15 December 1999

Revised: 15 December 2000

Published: 1 October 2001