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

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Kozlovski, O. and Strien, Sebastian van (2009) Local connectivity and quasi-conformal rigidity of non-renormalizable polynomials. Proceedings of the London Mathematical Society, Vol.99 (Part 2). pp. 275-296. doi:10.1112/plms/pdn055

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Official URL: http://dx.doi.org/10.1112/plms/pdn055

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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).

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
Official Date: September 2009
Dates:
DateEvent
September 2009Published
Volume: Vol.99
Number: Part 2
Number of Pages: 22
Page Range: pp. 275-296
DOI: 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

Data sourced from Thomson Reuters' Web of Knowledge

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