Computability of Brolin-Lyubich Measure

Ilia Binder, Mark Braverman, Cristobal Rojas, Michael Yampolsky

Resultado de la investigación: Contribución a una revistaArtículo

8 Citas (Scopus)

Resumen

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.

Idioma originalInglés
Páginas (desde-hasta)743-771
Número de páginas29
PublicaciónCommunications in Mathematical Physics
Volumen308
N.º3
DOI
EstadoPublicada - dic 2011

Áreas temáticas de ASJC Scopus

  • Física estadística y no lineal
  • Física matemática

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