Beyond topological hyperbolicity: The L-shadowing property
Beyond topological hyperbolicity: The L-shadowing property
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超越拓扑双曲性：L 阴影特性
DOI：
10.1016/j.jde.2019.09.052
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发表时间：
2019
影响因子：
2.4
通讯作者：
J. Vieitez
中科院分区：
文献类型：
--
作者：
A. Artigue;B. Carvalho;W. Cordeiro;J. Vieitez
本文进一步研究了[20]中定义的紧致空间上动力系统的L-跟踪性质。我们证明了二维球面的结构稳定的同构和一些伪Anosov同构满足这个性质。满足L-跟踪性质的同胚具有谱分解，其中基本集是可扩展的或包含任意小的拓扑半马蹄铁（限制与移位半共轭的周期集）。为此，我们使用局部稳定集和不稳定集以及经典跟踪性质来刻画L-跟踪性质。我们展示了同胚的L-跟踪性质和任意小的拓扑半马蹄没有周期点。最后，我们证明了正的有限膨胀性和跟踪性意味着空间是有限的。
In this paper we further explore the L-shadowing property defined in [20] for dynamical systems on compact spaces. We prove that structurally stable diffeomorphisms and some pseudo-Anosov diffeomorphisms of the two-dimensional sphere satisfy this property. Homeomorphisms satisfying the L-shadowing property have a spectral decomposition where the basic sets are either expansive or contain arbitrarily small topological semi-horseshoes (periodic sets where the restriction is semiconjugate to a shift). To this end, we characterize the L-shadowing property using local stable and unstable sets and the classical shadowing property. We exhibit homeomorphisms with the L-shadowing property and arbitrarily small topological semi-horseshoes without periodic points. At the end, we show that positive finite-expansivity jointly with the shadowing property imply that the space is finite.