C^{infty }$ 表面差分的 SRB 量纲

IF 2.6 1区数学 Q1 MATHEMATICS

Inventiones mathematicae Pub Date : 2024-02-05 DOI:10.1007/s00222-024-01235-7

引用次数: 0

摘要

摘要当且仅当集合 $\{ x, \limsup _{n}\frac{1}{n}\log \|d_{x}f^{n}\|>0}$具有正的 Lebesgue 度量时，一个 $C^{\infty }$光滑表面衍射才会有一个 SRB 度量。此外，遍历 SRB 度量的基点几乎无处不在地覆盖着这个 Lebesgue 集。对于具有$+\infty >r>1$的$C^{r}$曲面差分，我们也得到了类似的结果。

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SRB measures for $C^{\infty }$ surface diffeomorphisms

Abstract

A $C^{\infty }$ smooth surface diffeomorphism admits an SRB measure if and only if the set $\{ x, \ \limsup _{n}\frac{1}{n}\log \|d_{x}f^{n}\|>0\}$ has positive Lebesgue measure. Moreover the basins of the ergodic SRB measures are covering this set Lebesgue almost everywhere. We also obtain similar results for $C^{r}$ surface diffeomorphisms with $+\infty >r>1$ .

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来源期刊

Inventiones mathematicae 数学-数学

CiteScore

5.60

自引率

3.20%

发文量

审稿时长

12 months

期刊介绍： This journal is published at frequent intervals to bring out new contributions to mathematics. It is a policy of the journal to publish papers within four months of acceptance. Once a paper is accepted it goes immediately into production and no changes can be made by the author(s).