Local connectivity and quasi-conformal rigidity of non-renormalizable polynomials
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 0024-6115Full text not available from this repository.
Official URL: http://dx.doi.org/10.1112/plms/pdn055
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|
|Official Date:||September 2009|
|Number of Pages:||22|
|Page Range:||pp. 275-296|
|Access rights to Published version:||Restricted or Subscription Access|
|Funder:||Leverhulme Trust (LT), CODY, Leverhulme Trust Senior Fellowship|
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