The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes

DOI10.1007/s10240-011-0034-2zbMath1286.37047arXiv1005.4828OpenAlexW2063941378MaRDI QIDQ691694

Artur Avila, Mikhail Lyubich

Publication date: 3 December 2012

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.4828

zbMATH Keywords

renormalizationhybrid classtwo-sided shiftunicritical polynomial-like map

Mathematics Subject Classification ID

Universality and renormalization of dynamical systems (37E20) Renormalization of holomorphic dynamical systems (37F25)

Related Items (18)

The Lorenz Renormalization Conjecture ⋮ A period-doubling cascade precedes chaos for planar maps ⋮ The dynamics of complex box mappings ⋮ Regular or stochastic dynamics in families of higher-degree unimodal maps ⋮ Complex bounds for real maps ⋮ Parapuzzle of the Multibrot set and typical dynamics of unimodal maps ⋮ On the invariant Cantor sets of period doubling type of infinitely renormalizable area-preserving maps ⋮ Asymptotically holomorphic methods for infinitely renormalizable unimodal maps ⋮ A priori bounds for GIETs, affine shadows and rigidity of foliations in genus two ⋮ Asymmetric unimodal maps with non-universal period-doubling scaling laws ⋮ Pacman renormalization and self-similarity of the Mandelbrot set near Siegel parameters ⋮ Real bounds and quasisymmetric rigidity of multicritical circle maps ⋮ Rigidity for infinitely renormalizable area-preserving maps ⋮ Renormalization in one-dimensional dynamics ⋮ Lebesgue measure of Feigenbaum Julia sets ⋮ Dynamics of multicritical circle maps ⋮ Rigorous computer-assisted bounds on the period doubling renormalization fixed point and eigenfunctions in maps with critical point of degree 4 ⋮ Hyperbolicity of renormalization for dissipative gap mappings

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