一维逆极限的同胚及其在替换拼接、非稳定流形和帐篷映射中的应用
Homeomorphisms of One-dimensional Inverse Limits with Applications to Substitution Tilings, Unstable Manifolds, and Tent Maps
摘要：
假设f和g是马尔可夫满射，每个定义在一个楔形圆上，每个固定分支点，并将分支点作为唯一的临界值。我们证明了，如果对应于分支点的f和g的逆极限空间中的点是可区分的，那么这些逆极限空间是同胚的当且仅当f和g的替换是弱等价的.这一点和相关的结果，适用于一维替代平铺空间，一维非稳定流形的双曲集，和逆极限帐篷映射周期临界点。
英文摘要：
Suppose that f and g are Markov surjections, each defined on a wedge of circles, each fixing the branch point and having the branch point as the only critical value. We show that if the points in the inverse limit spaces associated with f and g corresponding to the branch point are distinguished then these inverse limit spaces are homeomorphic if and only if the substitutions associated with f and g are weakly equivalent. This, and related results, are applied to one-dimensional substitution tiling spaces, one-dimensional unstable manifolds of hyperbolic sets, and inverse limits of tent maps with periodic critical points.
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。
