The Combinatorial Rigidity Conjecture is False for Cubic Polynomials

Christian Henriksen

The Combinatorial Rigidity Conjecture is False for Cubic Polynomials

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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.

Original language	English
Journal	Trans. Amer. Math. Soc.
Volume	355
Issue number	9
Pages (from-to)	3625-3639
ISSN	0002-9947
Publication status	Published - 2003

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title = "The Combinatorial Rigidity Conjecture is False for Cubic Polynomials",

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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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

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