Submitted by math_admin on Sat, 02/22/2020 - 21:34
preprint-id:
preprint-title:
On the Quasisymmetrical Classification of Infinitely Renormalizable Maps: I. Maps with Feigenbaum's Topology
preprint-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.
preprint-year:
1991