On Julia sets of postcritically finite branched coverings Part II S<SUP>1</SUP>-parametrization of Julia sets

Atsushi KAMEYAMA

doi:10.2969/jmsj/1191419126

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

On Julia sets of postcritically finite branched coverings Part II

S¹-parametrization of Julia sets

Atsushi KAMEYAMA

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Keywords: Julia set, postcritically finite branched covering, S¹-parametrization, Thurston equivalence, mating

JOURNAL FREE ACCESS

2003 Volume 55 Issue 2 Pages 455-468

DOI https://doi.org/10.2969/jmsj/1191419126

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Abstract

We prove that for an expanding postcritically finite branched covering f, the Julia set is orientedly S¹-parametrizable if and only if fⁿ is combinatorially equivalent to the degenerate mating of two polynomials for some n>0.

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