SRB measures for $C^{\infty }$ surface diffeomorphisms
IF 4.6
Q2 MATERIALS SCIENCE, BIOMATERIALS
引用次数: 0
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 \(+\infty >r>1\) .
C^{infty }$ 表面差分的 SRB 量纲
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。
本文章由计算机程序翻译，如有差异，请以英文原文为准。
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