Computability of Brolin-Lyubich Measure

Ilia Binder, Mark Braverman, Cristobal Rojas, Michael Yampolsky

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

Brolin-Lyubich measure λR of a rational endomorphism R: Ĉ → Ĉ with deg R ≥ 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, the Brolin-Lyubich 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.

Original languageEnglish (US)
Pages (from-to)743-771
Number of pages29
JournalCommunications In Mathematical Physics
Volume308
Issue number3
DOIs
StatePublished - Dec 1 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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