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

Distortion results and invariant Cantor sets of unimodal maps