Piecewise expanding maps on the plane with singular ergodic properties

被引：16

作者：

Tsujii, M ^{[1
]}

机构：

[1] Hokkaido Univ, Dept Math, Sapporo, Hokkaido 0600810, Japan

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2000年 / 20卷

关键词：

D O I：

10.1017/S0143385700001012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For 1 less than or equal to r < <infinity>, we construct a piecewise C-r expanding map F : D --> D on the domain D = (0, 1) x (-1, 1) subset of R-2 with the following property: there exists an open set B in D such that the diameter of F-n(B) converges to 0 as n --> infinity and the empirical measure n(-1) Sigma (n-1)(k=0) delta (Fk(x)) converges to the point measure delta (p) at p = (0, 0) as n --> infinity for any point x is an element of B.

引用

页码：1851 / 1857

页数：7

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