Institute for Mathematical Sciences
M. Lyubich and A. Volberg
A Comparison of Harmonic and Balanced Measures on Cantor Repellors
Abstract: Let J be a Cantor repellor of a conformal map f. Provided f is a polynomial-like or R-symmetric, we prove that harmonic measure on J is equivalent to the measure of maximal entropy if and only if f is conformally equivalent to a polynomial. We also show that this is not true for general Cantor repellors: there is a non-polynomial algebraic function generating a Cantor repellor on which above two measures coincide.
View ims91-17 (PDF format)