ar X iv : 1 00 9 . 34 64 v 2 [ m at h . D S ] 9 N ov 2 01 0 COMPUTABILITY OF BROLIN - LYUBICH MEASURE
نویسنده
چکیده
Brolin-Lyubich measure λR of a rational endomorphism R : Ĉ → Ĉ with degR ≥ 2 is the unique invariant measure of maximal entropy hλR = htop(R) = log d. Its support is the Julia set J(R). We demonstrate that λR is always computable by an algorithm which has access to coefficients of R, even when J(R) is not computable. In the case when R is a polynomial, BrolinLyubich measure coincides with the harmonic measure of the basin of infinity. We find a sufficient condition for computability of the harmonic measure of a domain, which holds for the basin of infinity of a polynomial mapping, and show that computability may fail for a general domain.
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