同伦跟踪
Homotopy shadowing
摘要：
Michael Shub在1969年证明了紧致流形上的扩张自同态的拓扑共轭类是由它的同伦类型决定的。在这篇文章中，我们在两个方向上推广了这个结果。在一个方向上，我们考虑度量空间上的某些扩张映射。在第二个方向，我们考虑的地图是双曲的产品锥领域的产品流形。证明中的一个关键步骤是建立一个具有某些附加同伦信息的伪轨道的跟踪定理。
英文摘要：
Michael Shub proved in 1969 that the topological conjugacy class of an expanding endomorphism on a compact manifold is determined by its homotopy type. In this article we generalize this result in two directions. In one direction we consider certain expanding maps on metric spaces. In a second direction we consider maps which are hyperbolic with respect to product cone fields on a product manifold. A key step in the proof is to establish a shadowing theorem for pseudo--orbits with some additional homotopy information.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
