Satellite renormalization of quadratic polynomials

Autor:	Cheraghi, Davoud, Shishikura, Mitsuhiro
Rok vydání:	2015
Předmět:	Mathematics - Dynamical Systems Mathematics - Complex Variables Mathematics - Spectral Theory
Druh dokumentu:	Working Paper
Popis:	We prove the uniform hyperbolicity of the near-parabolic renormalization operators acting on an infinite-dimensional space of holomorphic transformations. This implies the universality of the scaling laws, conjectured by physicists in the 70's, for a combinatorial class of bifurcations. Through near-parabolic renormalizations the polynomial-like renormalizations of satellite type are successfully studied here for the first time, and new techniques are introduced to analyze the fine-scale dynamical features of maps with such infinite renormalization structures. In particular, we confirm the rigidity conjecture under a quadratic growth condition on the combinatorics. The class of maps addressed in the paper includes infinitely-renormalizable maps with degenerating geometries at small scales (lack of a priori bounds). Comment: 71 pages, comments welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1509.07843 Zobrazit plný text záznamu View this record from Arxiv