Article thumbnail
Location of Repository

Local connectivity and quasi-conformal rigidity of non-renormalizable polynomials

By O. Kozlovski and Sebastian van Strien

Abstract

We prove that topologically conjugate non-renormalizable polynomials are quasi-conformally conjugate. From this we derive that each such polynomial can be approximated by a hyperbolic polynomial. As a by-product we prove that the Julia set of a non-renormalizable polynomial with only hyperbolic periodic points is locally connected, and the Branner-Hubbard conjecture. The main tools are the enhanced nest construction (developed in a previous joint paper with [Rigidity for real polynomials, Ann. of Math. (2) 165 (2007) 749-841.]) and a lemma of Kahn and Lyubich (for which we give an elementary proof in the real case)

Topics: QA
Publisher: Cambridge University Press
Year: 2009
DOI identifier: 10.1112/plms/pdn055
OAI identifier: oai:wrap.warwick.ac.uk:17437
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://dx.doi.org/10.1112/plms... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.