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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 ISSN 0024-6115 .
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Official URL: http://dx.doi.org/10.1112/plms/pdn055
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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Proceedings of the London Mathematical Society | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 0024-6115 | ||||
Official Date: | September 2009 | ||||
Dates: |
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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 |
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