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Rigidity of harmonic measure

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Popovici I., Volberg A.

Fundamenta Mathematicae

1996

tom 150

nr 3

237-244

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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1 Fundamenta Mathematicae

1 Popovici I.

1 Volberg A.

1 1996

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Rigidity of harmonic measure