Pinching of polynomials.
type: Item
instance of: scholarly article
title: Pinching of polynomials.
zbMATH Open document ID: 1146.37347
author: Peter Haïssinsky
published in: Commentarii Mathematici Helvetici
publication date: 2002-06-17T00:00:00Z
review text: Summary: Let \(f_0: \mathbb{C} \to \mathbb{C}\) be a semi-hyperbolic polynomial in the sense of Carleson-Jones-Yoccoz with an attracting point. The goal of this paper is to show that one can define a semi-hyperbolic deformation \((f_t)_{t\geq 0}\) such that the attracting cycle becomes parabolic for the limit polynomial \(f_\infty\) and that \(f_0\) and \(f_\infty\) are semi-conjugate. This deformation is defined by pinching curves in appropriate quotient spaces.
Mathematics Subject Classification ID: 37F10
Mathematics Subject Classification ID: 30D05
Mathematics Subject Classification ID: 37F30
zbMATH DE Number: 1756812
zbMATH Keywords: Julia set
zbMATH Keywords: quasiconformal deformation
zbMATH Keywords: parabolic point
zbMATH Keywords: semi-hyperbolic polynomial
MaRDI profile type: Publication
full work available at URL: s00014-002-8329-z
OpenAlex ID: W2034991617
DOI: 10.1007/S00014-002-8329-Z
description: scientific article; zbMATH DE number 1756812