The Combinatorial Rigidity Conjecture is False for Cubic Polynomials

Christian Henriksen

The Combinatorial Rigidity Conjecture is False for Cubic Polynomials

Research output: Contribution to journal › Journal article › Research › peer-review

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

Cite this

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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.",

author = "Christian Henriksen",

year = "2003",

language = "English",

volume = "355",

pages = "3625--3639",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "9",

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T1 - The Combinatorial Rigidity Conjecture is False for Cubic Polynomials

AU - Henriksen, Christian

PY - 2003

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AB - 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.

M3 - Journal article

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EP - 3639

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 9

ER -