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Combinatorial rigidity for some infinitely renormalizable unicritical polynomials

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Cheraghi, Davoud (2010) Combinatorial rigidity for some infinitely renormalizable unicritical polynomials. Conformal Geometry and Dynamics, Vol.14 (No.13). pp. 219-255. doi:10.1090/S1088-4173-2010-00216-X ISSN 1088-4173.

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Official URL: http://dx.doi.org/10.1090/S1088-4173-2010-00216-X

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Abstract

Here we prove that infinitely renormalizable unicritical polynomials , with , satisfying a priori bounds and a certain ``combinatorial'' condition are combinatorially rigid. This implies the local connectivity of the connectedness loci (the Mandelbrot set when ) at the corresponding parameters.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title: Conformal Geometry and Dynamics
Publisher: American Mathematical Society
ISSN: 1088-4173
Official Date: 2010
Dates:
DateEvent
2010Published
Volume: Vol.14
Number: No.13
Page Range: pp. 219-255
DOI: 10.1090/S1088-4173-2010-00216-X
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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