Dynamics of certain smooth one-dimensional mappings I: The C^(1+α)-Denjoy-Koebe distortion lemma
classification
🧮 math.DS
keywords
distortionlemmaalphadenjoy-koebeone-dimensionalcertaincombinescomposition
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We prove a technical lemma, the $C^{1+\alpha }$-Denjoy-Koebe distortion lemma, estimating the distortion of a long composition of a $C^{1+\alpha }$ one-dimensional mapping $f:M\mapsto M$ 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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