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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2201.01268 |
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| _version_ | 1866915025137958912 |
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| author | Mercat, Paul |
| author_facet | Mercat, Paul |
| contents | For any primitive substitution whose Perron eigenvalue is Pisot unit, we construct a domain exchange measurably conjugated to the subshift. And we give a condition for the subshift to be a finite extension of a torus translation. For the particular case of weakly irreducible Pisot substitution, we show that the subshift is either a finite extension of a torus translation, either a power of the subshift is weakly mixing. And we provide an algorithm to compute eigenvalues of the subshift associated to any primitive pseudo-unimodular substitution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_01268 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Geometrical representation of subshifts for primitive substitutions Mercat, Paul Dynamical Systems 37B10, 37A05 For any primitive substitution whose Perron eigenvalue is Pisot unit, we construct a domain exchange measurably conjugated to the subshift. And we give a condition for the subshift to be a finite extension of a torus translation. For the particular case of weakly irreducible Pisot substitution, we show that the subshift is either a finite extension of a torus translation, either a power of the subshift is weakly mixing. And we provide an algorithm to compute eigenvalues of the subshift associated to any primitive pseudo-unimodular substitution. |
| title | Geometrical representation of subshifts for primitive substitutions |
| topic | Dynamical Systems 37B10, 37A05 |
| url | https://arxiv.org/abs/2201.01268 |