Complex a priori bounds revisited.
type: Item
instance of: scholarly article
title: Complex a priori bounds revisited.
zbMATH Open document ID: 1070.37029
author: Michael Yampolsky
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 2005-01-03T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73616
review text: The author studies the existence of complex a priori bounds for renormalizations of real quadratic polynomials. He introduces the combinatorial condition of essentially bounded type, which was the subject studied by the author and \textit{M. Lyubich} [Ann. Inst. Fourier (Grenoble) 47, 1219--1255 (1997; Zbl 0881.58053)] and gives a new treatment to polynomials satisfying this condition. The approach used in the paper is to consider them as small perturbations of parabolic maps, and to use the rigidity properties of such maps to pass from real a priori bounds to complex ones.
Mathematics Subject Classification ID: 37F25
Mathematics Subject Classification ID: 37E20
Mathematics Subject Classification ID: 37F50
Mathematics Subject Classification ID: 30D05
zbMATH DE Number: 2124652
zbMATH Keywords: real quadratic polynomials
zbMATH Keywords: complex a priori bounds
zbMATH Keywords: parabolic Julia sets
zbMATH Keywords: normalizations
zbMATH Keywords: perturbations of parabolic maps
zbMATH Keywords: rigidity
MaRDI profile type: Publication
OpenAlex ID: W1973075338
cites work: Q4383775
cites work: The set of maps \(F_{a,b}:x\mapsto x+a+{b\over 2\pi}\sin(2\pi x)\) with any given rotation interval is contractible
cites work: Parabolic limits of renormalization
cites work: Local connectivity of the Julia set of real polynomials
cites work: Combinatorics, geometry and attractors of quasi-quadratic maps
cites work: Dynamics of quadratic polynomials. I, II
cites work: Feigenbaum-Coullet-Tresser universality and Milnor's hairiness conjecture
cites work: Almost every real quadratic map is either regular or stochastic.
cites work: Dynamics of quadratic polynomials: complex bounds for real maps
cites work: Complex Dynamics and Renormalization (AM-135)
cites work: Renormalization and 3-Manifolds Which Fiber over the Circle
cites work: Q4271974
cites work: The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets
cites work: Q3476031
cites work: Q4264389
cites work: The attractor of renormalization and rigidity of towers of critical circle maps
DOI: 10.5802/AFST.1061
description: scientific article; zbMATH DE number 2124652