Measures of maximal relative entropy

2002/03/07 by Karl Petersen, Anthony Quas, Sujin Shin
Mathematics · #math.DS #math.PR #msc:37A05 #msc:37A35 #msc:37B10

paper · pdf

published as Erg. Th. Dyn. Sys. 23 (2003), 207-223. · 22 pages. (To appear in Erg. Th. Dyn. Sys.)

arxiv created 2002/03/07 · arxiv updated 2009/11/30

Abstract

Given an irreducible subshift of finite type X, a subshift Y, a factor map π: X → Y, and an ergodic invariant measure νon Y, there can exist more than one ergodic measure on X which projects to νand has maximal entropy among all measures in the fiber, but there is an explicit bound on the number of such maximal entropy preimages.

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