Entropy for Group Endomorphisms and Homogeneous Spaces

Abstract

Topological entropy h(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 hd(T) with measure theoretic entropy h(T); in particular h(T) = hd(T) for Haar measure and affine maps Ton compact metrizable groups. A particular case of this yields the wellknown formula for h(T) when T is a toral automorphism.