The equilibrium states for semigroups of rational maps

被引：12

作者：

Sumi, Hiroki ^{[2
]}

Urbanski, Mariusz ^{[1
]}

机构：

[1] Univ N Texas, Dept Math, Denton, TX 76203 USA

[2] Grad Sch Sci, Dept Math, Osaka 5600043, Japan

来源：

MONATSHEFTE FUR MATHEMATIK | 2009年 / 156卷 / 04期

关键词：

Rational semigroup; Skew product; Equilibrium state; JULIA SETS; FORM Z(2)+C(N); RANDOM ITERATIONS; POLYNOMIALS; DYNAMICS;

D O I：

10.1007/s00605-008-0016-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the dynamics of skew product maps associated with finitely generated semigroups of rational maps on the Riemann sphere. We show that under some conditions on the dynamics and the potential function psi, there exists a unique equilibrium state for psi and a unique exp(P(psi) - psi)-conformal measure, where P(psi) denotes the topological pressure of psi.

引用

页码：371 / 390

页数：20

共 21 条

[1]

[Anonymous], ERGOD THEOR DYN SYST

[2] Random iterations of polynomials of the form z2+cn:: connectedness of Julia sets [J].