Entropy for Group Endomorphisms and Homogeneous Spaces

Open Access

1 January 1971

journal article
Published by JSTOR in Transactions of the American Mathematical Society

Vol. 153, 401-414
https://doi.org/10.2307/1995565

Abstract

Topological entropy 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 with measure theoretic entropy ; in particular for Haar measure and affine maps on compact metrizable groups. A particular case of this yields the well-known formula for when is a toral automorphism.

Keywords

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