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ArticleOriginal scientific text

Title

Rigidity of harmonic measure

Authors 1, 1

Affiliations

  1. Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, U.S.A.

Abstract

Let J be the Julia set of a conformal dynamics f. Provided that f is polynomial-like we prove that the harmonic measure on J is mutually absolutely continuous with the measure of maximal entropy if and only if f is conformally equivalent to a polynomial. This is no longer true for generalized polynomial-like maps. But for such dynamics the coincidence of classes of these two measures turns out to be equivalent to the existence of a conformal change of variable which reduces the dynamical system to another one for which the harmonic measure equals the measure of maximal entropy.

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm150/fm15034.pdf

Fundamenta Mathematicae
1996/150/3
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Pages:
237-244
Main language of publication
English
Received
1995-04-28
Accepted
1995-12-29
Published
1996
Exact and natural sciences