The MathNet Korea
Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Duke Mathematical Journal
( Vol. 117 NO.2 / (2003))
Harmonic Measure and Polynomial Julia Sets
I. Binder, N. Makarov, S. Smirnov,
Pages. 343-365
Abstract There is a natural conjecture that the universal bounds for the dimension spectrum of
harmonic measure are the same for simply connected and for nonsimply connected
domains in the plane. Because of the close relation to conformal mapping theory, the
simply connected case is much better understood, and proving the above statement
would give new results concerning the properties of harmonic measure in the general case. \
We establish the conjecture in the category of domains bounded by polynomial
Julia sets. The idea is to consider the coefficients of the dynamical zeta function as
subharmonic functions on a slice of Teichmuller's space of the polynomial and then
to apply the maximum principle.
Contents 1. Dimension spectrum of harmonic measure
2. Branner-Hubbard families
3. Periodic cycles
Key words
Mathmatical Subject Classification 30C85, 37F10, 37F35