具有最终阴影性质的同胚的扩展测度

Pub Date : 2020-07-01 DOI:10.4134/JKMS.J190453
M. Dong, Keonhee Lee, Ngocthach Nguyen
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引用次数: 2

摘要

本文给出紧度量空间上同胚的Smale谱分解定理的一个可测版本。更确切地说,我们证明了如果紧度量空间X上的同纯态f在其链循环集CR(f)上是不变测度展开的,并且在CR(f)上具有最终阴影性质,则f具有谱分解。此外,我们还证明了f在X上是不变测度展开的当且仅当它对CR(f)的限制是不变测度展开。在此基础上,我们利用Ω-stability的概念对紧光滑流形上的扩展微分同态测度进行了刻画。
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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EXPANDING MEASURES FOR HOMEOMORPHISMS WITH EVENTUALLY SHADOWING PROPERTY
In this paper we present a measurable version of the Smale’s spectral decomposition theorem for homeomorphisms on compact metric spaces. More precisely, we prove that if a homeomorphism f on a compact metric space X is invariantly measure expanding on its chain recurrent set CR(f) and has the eventually shadowing property on CR(f), then f has the spectral decomposition. Moreover we show that f is invariantly measure expanding on X if and only if its restriction on CR(f) is invariantly measure expanding. Using this, we characterize the measure expanding diffeomorphisms on compact smooth manifolds via the notion of Ω-stability.
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