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Let X be a compact manifold and \(H(X)\) be its space of homeomorphisms. It is well known that a connected compact manifold of dimension \(>\,1\) is n-homogeneous. Using this, we study about the properties of the sets \(H(x,y)=\{h\in H(X) / h(O_f(x))= O_f(y)\}\) and \([x]=\bigcup _{y \in per_{n}(f)}{H(x,y)}\) where f is a continuous function and \(O_f(x)\) , \(per_{n}(f)\) denotes the orbit of x and the set of n-periodic points respectively.

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On the Space of Homeomorphisms of Connected Compact Manifolds

  • 会议论文

  • 发表日期：

    2025年

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  • T. J. Cinderella,
  • P. B. Vinod Kumar

摘要

Let X be a compact manifold and \(H(X)\) be its space of homeomorphisms. It is well known that a connected compact manifold of dimension \(>\,1\) is n-homogeneous. Using this, we study about the properties of the sets \(H(x,y)=\{h\in H(X) / h(O_f(x))= O_f(y)\}\) and \([x]=\bigcup _{y \in per_{n}(f)}{H(x,y)}\) where f is a continuous function and \(O_f(x)\) , \(per_{n}(f)\) denotes the orbit of x and the set of n-periodic points respectively.