Institute for Mathematical Sciences

Preprint ims91-17

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.
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