Limit sets, internal chain transitivity and orbital shadowing of tree-shifts defined on Markov-Cayley trees
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866907920744054784 |
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| author | Ban, Jung-Chao Huang, Nai-Zhu Lai, Guan-Yu |
| author_facet | Ban, Jung-Chao Huang, Nai-Zhu Lai, Guan-Yu |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20563 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limit sets, internal chain transitivity and orbital shadowing of tree-shifts defined on Markov-Cayley trees Ban, Jung-Chao Huang, Nai-Zhu Lai, Guan-Yu Dynamical Systems 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). |
| title | Limit sets, internal chain transitivity and orbital shadowing of tree-shifts defined on Markov-Cayley trees |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2405.20563 |