On the quasisymmetrical classification of infinitely renormalizable maps: I. Maps with Feigenbaum's topology.

Details On the quasisymmetrical classification of infinitely renormalizable maps: I. Maps with Feigenbaum's topology. On the quasisymmetrical classification of infinitely renormalizable maps: I. Maps with Feigenbaum's topology.

1991-10-11

arxiv.org/abs/math/9201294v1

Mathematics

Dynamical Systems

Scientific paper

A semigroup (dynamical system) generated by $C^{1+\alpha}$-contracting mappings is considered. We call a such semigroup regular if the maximum $K$ of the conformal dilatations of generators, the maximum $l$ of the norms of the derivatives of generators and the smoothness $\alpha$ of the generators satisfy a compatibility condition $K< 1/l^{\alpha}$. We prove the {\em geometric distortion lemma} for a regular semigroup generated by $C^{1+\alpha}$-contracting mappings.

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