Distortion results and invariant cantor sets of unimodal maps

Abstract

A distortion theory is developed for $S-$unimodal maps. It will be used to get some geometric understanding of invariant Cantor sets. In particular attracting Cantor sets turn out to have Lebesgue measure zero. Furthermore the ergodic behavior of $S-$unimodal maps is classified according to a distortion property, called the Markov-property.