Topological (\mathscrF,\mathscrG)-shadowing property

2025/07/05 by Joshi, Shital H., Shah, Ekta
#37B05 #37B65 #37B99 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.03982

Abstract

We define the concept of (\mathscrF,\mathscrG)-shadowing property on uniform space and say it as a topological (\mathscrF,\mathscrG)-shadowing property. We show that topological shadowing, topological (\mathscrD,\mathscrF_t)-shadowing, topological (\mathscrF_t,\mathscrF_t)-shadowing and topological (ℕ,\mathscrF_t)-shadowing are equivalent in compact chain recurrent dynamical system. We also prove that if minimal points of f are not dense in X then the system does not have (\mathscrP(ℕ),\mathscrF_ps)-shadowing.

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