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