Dynamics of Certain Smooth One-dimensional Mappings I. The C-Denjoy-Koebe distortion lemma

Abstract

We prove a technical lemma, the C-Denjoy-Koebe distortion lemma, estimating the distortion of a long composition of a C onedimensional mapping f : M 7→ M with finitely many, non-recurrent, power law critical points. The proof of this lemma combines the ideas of the distortion lemmas of Denjoy and Koebe. 

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