Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl

PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
• # Artykuł - szczegóły

## Fundamenta Mathematicae

2007 | 194 | 3 | 191-238

## Proximality in Pisot tiling spaces

EN

### Abstrakty

EN
A substitution φ is strong Pisot if its abelianization matrix is nonsingular and all eigenvalues except the Perron-Frobenius eigenvalue have modulus less than one. For strong Pisot φ that satisfies a no cycle condition and for which the translation flow on the tiling space $𝓣_{φ}$ has pure discrete spectrum, we describe the collection $𝓣^{P}_{φ}$ of pairs of proximal tilings in $𝓣_{φ}$ in a natural way as a substitution tiling space. We show that if ψ is another such substitution, then $𝓣_{φ}$ and $𝓣_{ψ}$ are homeomorphic if and only if $𝓣^{P}_{φ}$ and $𝓣^{P}_{ψ}$ are homeomorphic. We make use of this invariant to distinguish tiling spaces for which other known invariants are ineffective. In addition, we show that for strong Pisot substitutions, pure discrete spectrum of the flow on the associated tiling space is equivalent to proximality being a closed relation on the tiling space.

191-238

wydano
2007

### Twórcy

autor
• Department of Mathematics, Montana State University, Bozeman, MT 59717, U.S.A.
autor
• Department of Mathematics, College of Charleston, Charleston, SC 29424, U.S.A.