Examples of expandingC1 maps having no σ-finite invariant measure equivalent to Lebesgue

被引：0
作者：
Henk Bruin
Jane Hawkins
机构：
[1] Royal Institute of Technology,Department of Mathematics
[2] University of North Carolina at Chapel Hill,Department of Mathematics
来源：
Israel Journal of Mathematics | 1998年 / 108卷
关键词：
Lebesgue Measure; Invariant Measure; Invariant Probability Measure; Critical Orbit; Ergodic Component;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we construct aC1 expanding circle map with the property that it has no σ-finite invariant measure equivalent to Lebesgue measure. We extend the construction to interval maps and maps on higher dimensional tori and the Riemann sphere. We also discuss recurrence of Lebesgue measure for the family of tent maps.
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页码：83 / 107
页数：24
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