2023/12/22 by Ritong Li, Dongkui Ma, Li, Ritong +5
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2312.14444
openalex publication_date 2023/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The shadowable points of dynamical systems has been well-studied by Morales \citeMR3535492. This paper aims to generalize the main results obtained by Morales to free semigroup actions. To this end, we introduce the notion of shadowable points of a free semigroup action. Let G be a free semigroup generated by finite continuous self-maps acting on compact metric space. We will prove the following results for G on compact metric spaces. The set of shadowable points of G is a Borel set. G has the pseudo-orbit tracing property (POTP) if and only if every point is a shadowable point of G. The chain recurrent and non-wandering sets of G coincide when every chain recurrent point is a shadowable point of G. The space X is totally disconnected at every shadowable point of G under certain condition.