Historic Behaviour for Random Expanding Maps on the Circle

被引：2

作者：

Nakano, Yushi ^{[1
,2
]}

机构：

[1] Osaka City Univ, Osaka, Japan

[2] Kitami Inst Technol, Fac Engn, Kitami, Hokkaido 0908507, Japan

来源：

TOKYO JOURNAL OF MATHEMATICS | 2017年 / 40卷 / 01期

关键词：

Historic behaviour; Random expanding maps; AVERAGES;

D O I：

10.3836/tjm/1502179221

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

F. Takens constructed a residual subset of the state space consisting of initial points with historic behaviour for expanding maps on the circle. We prove that this statistical property of expanding maps on the circle is preserved under small random perturbations. The proof is given by establishing a random Markov partition, which follows from a random version of Shub's Theorem on topological conjugacy with the folding maps.

引用

页码：165 / 184

页数：20

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