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

Yunping Jiang

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

Dynamical Systems 2016-09-06 v1

Authors: Yunping Jiang

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.

Keywords

quasisymmetrical classification infinitely renormalizable maps feigenbaum topology regular semigroup contracting mappings geometric distortion lemma conformal dilatation

Cite

@article{arxiv.math/9201294,
  title  = {On the quasisymmetrical classification of infinitely renormalizable maps: I. Maps with Feigenbaum's topology.},
  author = {Yunping Jiang},
  journal= {arXiv preprint arXiv:math/9201294},
  year   = {2016}
}

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

Abstract

Keywords

Cite

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