Geometric study of the beta-integers for a Perron number and mathematical quasicrystals
نویسندگان
چکیده
منابع مشابه
Geometric study of the beta - integers for a Perron number and mathematical quasicrystals par
Ŕ́. Nous étudions géométriquement les ensembles de points de R obtenus par la betanumération que sont les β-entiers Zβ ⊂ Z[β] où β est un nombre de Perron. Nous montrons qu’il existe deux schémas de coupe-et-projection canoniques associés à la β-numération, où les β-entiers se relèvent en certains points du réseau Z (m = degré de β) , situés autour du sous-espace propre dominant de la matri...
متن کاملde Théorie des Nombres de Bordeaux 16 ( 2004 ) , 125 – 149 Geometric study of the beta - integers for a Perron number and mathematical quasicrystals par
We investigate in a geometrical way the point sets of R obtained by the β-numeration that are the β-integers Zβ ⊂ Z[β] where β is a Perron number. We show that there exist two canonical cut-and-project schemes associated with the β-numeration, allowing to lift up the β-integers to some points of the lattice Z (m = degree of β) lying about the dominant eigenspace of the companion matrix of β . W...
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We investigate in a geometrical way the sieving process of 021 β 3 for obtaining the Delone set 0 β 4 051 β 3 of β integers where β is a Perron number in the context of linear asymptotic invariants associated with a canonical inductive system constructed from β . When β is a Pisot number, we exhibit a canonical cut-and-project scheme, a model set associated with 0 β and so prove that it is a Me...
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2004
ISSN: 1246-7405
DOI: 10.5802/jtnb.437