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A variation on the variational principle and applications to entropy pairs

Published online by Cambridge University Press:  17 April 2001

F. BLANCHARD,
E. GLASNER and
B. HOST
F. BLANCHARD
Affiliation:
LMD-CNRS, case 930, 163 avenue de Luminy, 13288 Marseille Cedex 09, France
E. GLASNER
Affiliation:
School of Mathematics, Tel Aviv University, Tel Aviv 69978, Israel
B. HOST
Affiliation:
LMD-CNRS, case 930, 163 avenue de Luminy, 13288 Marseille Cedex 09, France
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Abstract

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The variationalprinciple states that the topological entropy of a topological dynamical systemis equal to the sup of the entropies of invariant measures. It is proved thatfor any finite open cover there is an invariant measure such that thetopological entropy of this cover is less than or equal to the entropiesof all finer partitions. One consequence of thisresult is that for any dynamical system with positive topological entropy thereexists an invariant measure whose set of entropy pairs is equal to the set oftopological entropy pairs.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 1 , February 1997, pp. 29 - 43
Copyright
1997 Cambridge University Press