Topological conditions for the existence of absorbing Cantor sets

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