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

Abstract

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.

References in corpus (1)

• Dynamics of certain smooth one-dimensional mappings II: geometrically finite one-dimensional mappings