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 original | English |
|---|---|
| Páginas (desde-hasta) | 743-771 |
| Número de páginas | 29 |
| Publicación | Communications in Mathematical Physics |
| Volumen | 308 |
| N.º | 3 |
| DOI | |
| Estado | Published - dic 2011 |
Huella dactilar
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
Citar esto
}
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
TY - JOUR
T1 - Computability of Brolin-Lyubich Measure
AU - Binder, Ilia
AU - Braverman, Mark
AU - Rojas, Cristobal
AU - Yampolsky, Michael
PY - 2011/12
Y1 - 2011/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=80955134005&partnerID=8YFLogxK
U2 - 10.1007/s00220-011-1363-1
DO - 10.1007/s00220-011-1363-1
M3 - Article
AN - SCOPUS:80955134005
VL - 308
SP - 743
EP - 771
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 3
ER -