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Entropy pairs for a measure

Published online by Cambridge University Press:  19 September 2008

F. Blanchard ,
B. Host ,
A. Maass ,
S. Martinez  and
D. J. Rudolph
F. Blanchard
Affiliation:
CNRS, Laboratoire de Mathématiques Discrètes-Case 930–163 avenue de Luminy-13288 Marseille Cedex 09, France
B. Host
Affiliation:
Université d-Aix-Marseille II and Laboratoire de Mathématiques Discrétes-Case 930–163 avenue de Luminy-13288 Marseille Cedex 09, France
A. Maass
Affiliation:
CNRS-Laboratoire de Mathématiques Discrètes-Case 930–163 avenue de Luminy-13288 Marseille Cedex 09, France and Departamento de Ingenieria Matemàtica, Universidad de Chile, Casilla 170/3 Correo 3, Santiago, Chile
S. Martinez
Affiliation:
Universidad de Chile, Casilla 170/3 Correo 3, Santiago, Chile
D. J. Rudolph
Affiliation:
Mathematics Department, University of Maryland, College Park, Md 20742, USA and Laboratoire de Mathématiques Discrètes-Case 930–163 avenue de Luminy-13288 Marseille Cedex 09, France
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Abstract

We define entropy pairs for an invariant measure µ on a topological dynamical system (X, T), and show they allow one to construct the maximal topological factorwith entropy 0 for µ. Then we prove that for any µ, a µ-entropy pair is always topologically so, and the reverse is true when (X, T) is uniquely ergodic.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 4 , August 1995 , pp. 621 - 632
Copyright
Copyright © Cambridge University Press 1995

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References

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