Limit sets, internal chain transitivity and orbital shadowing of tree-shifts defined on Markov-Cayley trees

2024/05/31 by Jung‐Chao Ban, Ban, Jung-Chao, Nai-Zhu Huang +3
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2405.20563

openalex publication_date 2024/05/31 · openalex created_date 2024/06/04 · openalex updated_date 2026/08/01

Abstract

In this paper, we introduce the concepts of ω-limit sets and pseudo orbits for a tree-shift defined on a Markov-Cayley tree, extending the results of tree-shifts defined on d-trees [5,6]. Firstly, we establish the relationships between ω-limit sets and we introduce a modified definition of ω-limit set based on complete prefix sets (Theorems 1.4 and 1.9). Secondly, we introduce the concept of projected pseudo orbits and investigate the concept of the shadowing property (Theorems 1.12 and 1.14).

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