Geodesic
Rigidity of harmonic measure
Fundamenta Mathematicae, Tome 150 (1996) no. 3, pp. 237-244.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm-150-3-237-244

I. Popovici 1 ; A. Volberg 1

1 
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I. Popovici; A. Volberg. Rigidity of harmonic measure. Fundamenta Mathematicae, Tome 150 (1996) no. 3, pp. 237-244. doi : 10.4064/fm-150-3-237-244. http://geodesic.mathdoc.fr/articles/10.4064/fm-150-3-237-244/

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