发表机构
School of Mathematics, Sun Yat-sen University; Hangzhou International Innovation Institute of Beihang University; School of Mathematics (Zhuhai), Sun Yat-sen University; School of Mathematics and Statistics, Liaoning University（中山大学数学学院; 北京航空航天大学杭州国际创新研究院; 中山大学（珠海）数学学院; 辽宁大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明Anosov微分同胚具有拓扑扩张性，并揭示Lipschitz阴影性与一致横截性及阴影常数的定量联系，同时给出两个反例说明扩张性与阴影性在完备黎曼流形上并非等价。
AI 中文摘要
我们证明了每个Anosov微分同胚在[9]的意义下都是拓扑扩张的。我们还证明了Lipschitz阴影性迫使稳定丛和不稳定丛一致横截，并给出了用阴影常数表示的定量界。最后，我们在完备黎曼流形上给出两个例子：一个是扩张的但不具有阴影性，另一个具有有限体积、有界截面曲率、Lipschitz阴影性和正交不变丛，但相对于其黎曼距离不是扩张的。
英文摘要
We show that every Anosov diffeomorphism is topologically expansive in the sense of [9]. We also prove that Lipschitz shadowing forces the stable and unstable bundles to be uniformly transverse, with a quantitative bound in terms of the shadowing constant. Finally, we give two examples on complete Riemannian manifolds: one is expansive but does not have the shadowing property, while the other has finite volume, bounded sectional curvature, Lipschitz shadowing, and orthogonal invariant bundles, but is not expansive with respect to its Riemannian distance.
