Multifractal formalism for expanding rational semigroups and random complex dynamical systems

被引：7
|
作者：
Jaerisch, Johannes [1 ]
Sumi, Hiroki [2 ]
机构：
[1] Shimane Univ, Dept Math, Fac Sci & Engn, Matsue, Shimane 6908504, Japan
[2] Osaka Univ, Dept Math, Grad Sch Sci, Toyonaka, Osaka 5600043, Japan
来源：
NONLINEARITY | 2015年 / 28卷 / 08期
基金：
奥地利科学基金会;
关键词：
complex dynamical systems; rational semigroups; random complex dynamics; multifractal formalism; Julia set; Hausdorff dimension; random iterations; MAPS; DIMENSION;
D O I：
10.1088/0951-7715/28/8/2913
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the multifractal formalism for the dynamics of semigroups of rational maps on the Riemann sphere and random complex dynamical systems. We elaborate a multifractal analysis of level sets given by quotients of Birkhoff sums with respect to the skew product associated with a semigroup of rational maps. Applying these results, we perform a multifractal analysis of the Holder regularity of limit state functions of random complex dynamical systems.
引用
收藏
页码：2913 / 2938
页数：26
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