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Distortion results and invariant Cantor sets of unimodal maps. (English) Zbl 0809.58026
The author proves that Cantor attractors of \(S\)-unimodal maps have Lebesgue measure zero. A distortion theory is developed for these maps. It is proved, that every \(S\)-unimodal map not having periodic attractors has weak-Markov property (this means, that the map has uniform good distortion properties).

MSC:
37A99 Ergodic theory
37D99 Dynamical systems with hyperbolic behavior
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