Computability of Brolin-Lyubich Measure

Ilia Binder, Mark Braverman, Cristobal Rojas, Michael Yampolsky

Resultado de la investigación: Article

6 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 originalEnglish
Páginas (desde-hasta)743-771
Número de páginas29
PublicaciónCommunications in Mathematical Physics
Volumen308
N.º3
DOI
EstadoPublished - dic 2011

Huella dactilar

Harmonic Measure
Computability
Infinity
Polynomial Mapping
Julia set
Endomorphism
Invariant Measure
infinity
Entropy
polynomials
Polynomial
Sufficient Conditions
Coefficient
harmonics
Demonstrate
entropy
coefficients

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Citar esto

Binder, Ilia ; Braverman, Mark ; Rojas, Cristobal ; Yampolsky, Michael. / Computability of Brolin-Lyubich Measure. En: Communications in Mathematical Physics. 2011 ; Vol. 308, N.º 3. pp. 743-771.
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Computability of Brolin-Lyubich Measure. / Binder, Ilia; Braverman, Mark; Rojas, Cristobal; Yampolsky, Michael.

En: Communications in Mathematical Physics, Vol. 308, N.º 3, 12.2011, p. 743-771.

Resultado de la investigación: Article

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