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A continuous map on the topological space X can have a dense set of periodic points with the periods being \(\mathbb {Z+}\) . In this paper, such maps are called Periodically Rich maps. We show that the Periodically Rich maps on interval is divided into two classes. It is shown that every compact manifold of dimension greater than or equal to one admits Periodically Rich maps.

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On Maps with Dense Periodic Points and Set of Periods \(\mathbb {Z+}\)

  • 会议论文

  • 发表日期：

    2025年

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  • Suja N. Thomas,
  • P. B. Vinod Kumar

摘要

A continuous map on the topological space X can have a dense set of periodic points with the periods being \(\mathbb {Z+}\) . In this paper, such maps are called Periodically Rich maps. We show that the Periodically Rich maps on interval is divided into two classes. It is shown that every compact manifold of dimension greater than or equal to one admits Periodically Rich maps.