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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Entropy for group endomorphisms and homogeneous spaces

Author: Rufus Bowen
Journal: Trans. Amer. Math. Soc. 153 (1971), 401-414
MSC: Primary 28.70; Secondary 22.00
Erratum: Trans. Amer. Math. Soc. 181 (1973), 509-510.
MathSciNet review: 0274707
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Abstract: Topological entropy $ {h_d}(T)$ is defined for a uniformly continuous map on a metric space. General statements are proved about this entropy, and it is calculated for affine maps of Lie groups and certain homogeneous spaces. We compare $ {h_d}(T)$ with measure theoretic entropy $ h(T)$; in particular $ h(T) = {h_d}(T)$ for Haar measure and affine maps $ T$ on compact metrizable groups. A particular case of this yields the well-known formula for $ h(T)$ when $ T$ is a toral automorphism.

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Keywords: Entropy, $ T$-homogeneous measure
Article copyright: © Copyright 1971 American Mathematical Society