Kozlovski, O. and van Strien, Sebastian. (2009) Local connectivity and quasi-conformal rigidity of non-renormalizable polynomials. Proceedings of the London Mathematical Society, Vol.99 (Part 2). pp. 275-296. ISSN 0024-6115

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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).

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Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Proceedings of the London Mathematical Society
Publisher:	Cambridge University Press
ISSN:	0024-6115
Date:	September 2009
Volume:	Vol.99
Number:	Part 2
Number of Pages:	22
Page Range:	pp. 275-296
Identification Number:	10.1112/plms/pdn055
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Leverhulme Trust (LT), CODY, Leverhulme Trust Senior Fellowship
URI:	http://wrap.warwick.ac.uk/id/eprint/17437

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