Coboundaries and eigenvalues of morphic subshifts
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916216874991616 |
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| author | Mercat, Paul |
| author_facet | Mercat, Paul |
| contents | We define a morphic subshift as a subshift generated by the image of a substitution subshift by another substitution. In other words, it is the subshift associated with a ultimately periodic directive sequence. We present an efficient algorithm for computing eigenvalues of morphic subshifts using coboundaries. We show that continuous eigenvalues of S-adic subshifts for primitive directive sequences are always associated with some coboundary. For morphic subshifts, we provide a characterization of the dimension of the Q-vector space generated by eigenvalues. Additionally, if the substitutions are unimodular and without coboundaries, we give a necessary and sufficient condition for weak mixing of the subshift. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13656 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coboundaries and eigenvalues of morphic subshifts Mercat, Paul Dynamical Systems We define a morphic subshift as a subshift generated by the image of a substitution subshift by another substitution. In other words, it is the subshift associated with a ultimately periodic directive sequence. We present an efficient algorithm for computing eigenvalues of morphic subshifts using coboundaries. We show that continuous eigenvalues of S-adic subshifts for primitive directive sequences are always associated with some coboundary. For morphic subshifts, we provide a characterization of the dimension of the Q-vector space generated by eigenvalues. Additionally, if the substitutions are unimodular and without coboundaries, we give a necessary and sufficient condition for weak mixing of the subshift. |
| title | Coboundaries and eigenvalues of morphic subshifts |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2404.13656 |