Topological Conditions for the Existence of Absorbing Cantor Sets

This paper deals with strange attractors of S-unimodal maps f . It generalizes results from [BKNS] in the sense that very general topological conditions are given that either i) guarantee the existence of an absorbing Cantor set provided the critical point of f is sufficiently degenerate, or ii) prohibit the existence of an absorbing Cantor set altogether. As a byproduct we obtain very weak topological conditions that imply the existence of an absolutely continuous invariant probability measure for f .