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Transfer operator, topological entropy and maximal measure for cocyclic subshifts

Published online by Cambridge University Press:  09 August 2004

JAROSLAW KWAPISZ
JAROSLAW KWAPISZ
Affiliation:
Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717-2400, USA (e-mail: jarek@math.montana.edu)
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Abstract

Cocyclic subshifts arise as the supports of matrix cocycles over a full shift and generalize topological Markov chains and sofic systems. We compute the topological entropy of a cocyclic subshift as the logarithm of the spectral radius of an appropriate transfer operator and give a concrete description of the measure of maximal entropy in terms of the eigenvectors. Unlike in the Markov or sofic case, the operator is infinite-dimensional and the entropy may be a logarithm of a transcendental number.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 4 , August 2004 , pp. 1173 - 1197
Copyright
2004 Cambridge University Press

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