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The combinatorial rigidity conjecture is false for cubic polynomials


Author: Christian Henriksen
Journal: Trans. Amer. Math. Soc. 355 (2003), 3625-3639
MSC (2000): Primary 37F10; Secondary 37F20, 37F45
Published electronically: May 29, 2003
MathSciNet review: 1990165
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that there exist two cubic polynomials with connected Julia sets which are combinatorially equivalent but not topologically conjugate on their Julia sets. This disproves a conjecture by McMullen from 1995.


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Additional Information

Christian Henriksen
Affiliation: Université Paul Sabatier, Laboratoire Emile Picard, 118, route de Narbonne, 31062 Toulouse Cedex, France
Address at time of publication: Department of Mathematics, Technical University of Denmark, Matematiktorvet, building 303, DK - 2800 Kgs Lyngby, Denmark
Email: chris@picard.ups-tlse.fr, christian.henriksen@mat.dtu.dk

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03259-8
Received by editor(s): January 30, 2002
Received by editor(s) in revised form: August 13, 2002
Published electronically: May 29, 2003
Additional Notes: This research was funded by a Marie Curie Fellowship
Article copyright: © Copyright 2003 American Mathematical Society