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Measures of maximal relative entropy

Published online by Cambridge University Press:  24 January 2003

KARL PETERSEN ,
ANTHONY QUAS  and
SUJIN SHIN
KARL PETERSEN
Affiliation:
Department of Mathematics, CB 3250, Phillips Hall, University of North Carolina, Chapel Hill, NC 27599, USA (e-mail: petersen@math.unc.edu)
ANTHONY QUAS
Affiliation:
Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152-6429, USA (e-mail: quasa@msci.memphis.edu)
SUJIN SHIN
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3P4, Canada and Department of Mathematics, Ajou University, Suwon 422-749, South Korea (e-mail: sjs@math.kaist.ac.kr) Current address: Department of Mathematics, Korea Advanced Institute of Science and Technology, Daejon 305-701, South Korea
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Abstract

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

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 1 , February 2003 , pp. 207 - 223
Copyright
2003 Cambridge University Press