Spectral decomposition and Ω-stability of flows with expanding measures
Spectral decomposition and Ω-stability of flows with expanding measures
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具有扩展措施的流谱分解和 Ω 稳定性
DOI：
10.1016/j.jde.2020.06.002
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发表时间：
2020
影响因子：
2.4
通讯作者：
Ngocthach Nguyen
中科院分区：
文献类型：
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作者：
Keonhee Lee;Ngocthach Nguyen
在本文中，我们提出了流的经典谱分解定理的可测量版本。更准确地说，我们证明，如果紧致度量空间 X 上的流 ψ 在其链循环集 C R (ψ) 上不变地测度扩展，并且在 C R (ψ) 上具有不变测度遮蔽性质，则 ψ 具有谱分解，即非游走集 Ω (ψ) 由有限多个不变和闭子集的不相交并分解，其中 ψ 是拓扑传递的。此外，我们还表明，如果 phi 是在 C R (phi) 上不变的测度扩展，那么它是在 X 上不变的测度扩展。利用这一点，我们通过 Ω 稳定性的概念来表征紧致 C∞ 流形上的测度扩展流。
In this paper we present a measurable version of the classical spectral decomposition theorem for flows. More precisely, we prove that if a flow ϕ on a compact metric space X is invariantly measure expanding on its chain recurrent set C R (ϕ) and has the invariantly measure shadowing property on C R (ϕ) then ϕ has the spectral decomposition, ie the nonwandering set Ω (ϕ) is decomposed by a disjoint union of finitely many invariant and closed subsets on which ϕ is topologically transitive. Moreover we show that if ϕ is invariantly measure expanding on C R (ϕ) then it is invariantly measure expanding on X. Using this, we characterize the measure expanding flows on a compact C∞ manifold via the notion of Ω-stability.
影响因子：
2.4
作者：
通讯作者：
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