Entropy for group endomorphisms and homogeneous spaces

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