In this paper we further explore the L-shadowing property defined in [17] 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.

中文翻译：

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超越拓扑双曲线：L-shadowing 属性

在本文中，我们进一步探讨了 [17] 中为紧凑空间上的动态系统定义的 L 阴影属性。我们证明了二维球体的结构稳定微分同胚和一些伪阿诺索夫微分同胚满足这个性质。满足 L 阴影性质的同胚具有谱分解，其中基本集要么是膨胀的，要么包含任意小的拓扑半马蹄形（限制与位移半共轭的周期集）。为此，我们使用局部稳定和不稳定集以及经典阴影属性来表征 L 阴影属性。我们展示了具有 L 阴影特性的同胚和任意小的没有周期点的拓扑半马蹄形。在最后，