To Symbolic Dynamics Through The Thue-Morse Sequence
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866929240669159424 |
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| author | Pannipitiya, Diyath |
| author_facet | Pannipitiya, Diyath |
| contents | The celebrated Thue-Morse sequence, or the Prouhet-Thue-Morse sequence (A010060 in the OEIS), has a number of interesting properties and is a rich source to many (counter)examples. We introduce two different square-free sequences on three letters with one of them is equivalent (up-to permutations of letters) to Thue's original square-free sequence on three letters. Then we use them to introduce an explicit method to construct infinitely many number of recurrent points in ${\{0,1\}^{\mathbb{N}}}$ whose orbit closures under the shift map is minimal, uncountable, and for any two distinct such points their orbit closures are disjoint. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07015 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | To Symbolic Dynamics Through The Thue-Morse Sequence Pannipitiya, Diyath Dynamical Systems The celebrated Thue-Morse sequence, or the Prouhet-Thue-Morse sequence (A010060 in the OEIS), has a number of interesting properties and is a rich source to many (counter)examples. We introduce two different square-free sequences on three letters with one of them is equivalent (up-to permutations of letters) to Thue's original square-free sequence on three letters. Then we use them to introduce an explicit method to construct infinitely many number of recurrent points in ${\{0,1\}^{\mathbb{N}}}$ whose orbit closures under the shift map is minimal, uncountable, and for any two distinct such points their orbit closures are disjoint. |
| title | To Symbolic Dynamics Through The Thue-Morse Sequence |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2402.07015 |