The Pisot conjecture for -substitutions
We prove the Pisot conjecture for $\unicode[STIX]{x1D6FD}$ -substitutions: if $\unicode[STIX]{x1D6FD}$ is a Pisot number, then the tiling dynamical system $(\unicode[STIX]{x1D6FA}_{\unicode[STIX]{x1D713}_{\unicode[STIX]{x1D6FD}}},\mathbb{R})$ associated with the $\unicode[STIX]{x1D6FD}$ -substitutio...
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| Vydáno v: | Ergodic theory and dynamical systems Ročník 38; číslo 2; s. 444 - 472 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Cambridge
Cambridge University Press
01.04.2018
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| Témata: | |
| ISSN: | 0143-3857, 1469-4417 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | We prove the Pisot conjecture for $\unicode[STIX]{x1D6FD}$ -substitutions: if $\unicode[STIX]{x1D6FD}$ is a Pisot number, then the tiling dynamical system $(\unicode[STIX]{x1D6FA}_{\unicode[STIX]{x1D713}_{\unicode[STIX]{x1D6FD}}},\mathbb{R})$ associated with the $\unicode[STIX]{x1D6FD}$ -substitution has pure discrete spectrum. As corollaries: (1) arithmetical coding of the hyperbolic solenoidal automorphism associated with the companion matrix of the minimal polynomial of any Pisot number is almost everywhere one-to-one; and (2) all Pisot numbers are weakly finitary. |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0143-3857 1469-4417 |
| DOI: | 10.1017/etds.2016.44 |