EXPANDING MEASURES FOR HOMEOMORPHISMS WITH EVENTUALLY SHADOWING PROPERTY
EXPANDING MEASURES FOR HOMEOMORPHISMS WITH EVENTUALLY SHADOWING PROPERTY
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扩展同态测量并最终实现阴影特性
DOI：
10.4134/jkms.j190453
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发表时间：
2020
影响因子：
0.6
通讯作者：
Ngocthach Nguyen
中科院分区：
文献类型：
--
作者：
M. Dong;Keonhee Lee;Ngocthach Nguyen
本文给出了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上的同胚f在其链递归集CR（f）上是不变测度扩张的，并且在CR（f）上具有最终跟踪性质，则f具有谱分解.证明了f在X上是不变测度扩张的当且仅当它对CR（f）的限制是不变测度扩张的.在此基础上，我们利用Ω-稳定性的概念刻画了紧致光滑流形上的测度扩张超同态。
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.