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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
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: |
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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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