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Displaying similar documents to “Invariant sets for 𝒜 -harmonic measure.”

Rigidity of harmonic measure

I. Popovici, Alexander Volberg (1996)

Fundamenta Mathematicae

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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...