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Entropy of a symbolic extension of a dynamical system

Published online by Cambridge University Press:  06 August 2001

TOMASZ DOWNAROWICZ
TOMASZ DOWNAROWICZ
Affiliation:
Institute of Mathematics, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, PL-50-370 Wroclaw, Poland (e-mail: [email protected])
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Abstract

Residual entropy of a topological system is defined as the infimum increase of entropy necessary to build a symbolic extension of this system. If no symbolic extension exists then residual entropy is set at infinity. In this paper we provide a direct formula for the residual entropy of a system on a totally disconnected compact space in terms of basic notions of conditional entropies viewed as functions of invariant measures. This formula allows us to evaluate residual entropy in many examples as well as to construct new examples with arbitrarily preset topological and residual entropies. The appendix contains a condition equivalent to asymptotic h-expansiveness.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 4 , August 2001 , pp. 1051 - 1070
Copyright
2001 Cambridge University Press

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