Displaying similar documents to “On supports of dynamical laminations and biaccessible points in polynomial Julia sets”

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...

Transfinite diameter, Chebyshev constants, and capacities in ℂⁿ

Vyacheslav Zakharyuta (2012)

Annales Polonici Mathematici

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The famous result of geometric complex analysis, due to Fekete and Szegö, states that the transfinite diameter d(K), characterizing the asymptotic size of K, the Chebyshev constant τ(K), characterizing the minimal uniform deviation of a monic polynomial on K, and the capacity c(K), describing the asymptotic behavior of the Green function g K ( z ) at infinity, coincide. In this paper we give a survey of results on multidimensional notions of transfinite diameter, Chebyshev constants and capacities,...