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This chapter presents a study of orbital maps in the context of semigroup actions on topological spaces. It is introduced a class of orbital maps which is related to the asymptotical behavior of semigroup actions. By considering this class of maps, the behavior of limit sets, prolongations, prolongational limit sets, domains and regions of attraction, attractors, and Lyapunov stable sets under continuous orbital maps is investigated.

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Orbital Maps

  • 章节

  • 发表日期：

    2025年

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  • Victor H. L. Rocha,
  • Josiney A. Souza

摘要

This chapter presents a study of orbital maps in the context of semigroup actions on topological spaces. It is introduced a class of orbital maps which is related to the asymptotical behavior of semigroup actions. By considering this class of maps, the behavior of limit sets, prolongations, prolongational limit sets, domains and regions of attraction, attractors, and Lyapunov stable sets under continuous orbital maps is investigated.