Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-12-04T00:23:29.643Z Has data issue: false hasContentIssue false

Two-symbol Pisot substitutions have pure discrete spectrum

Published online by Cambridge University Press:  22 September 2003

MICHAEL HOLLANDER
Affiliation:
23-08 Newtown Rd #3F West, Long Island City, NY 11102, USA
BORIS SOLOMYAK
Affiliation:
Box 354350, Department of Mathematics, University of Washington, Seattle, WA 98195, USA (e-mail: solomyak@math.washington.edu)

Abstract

We show that any Pisot substitution dynamical system on two symbols has pure discrete spectrum. This follows from an analysis of a combinatorial ‘balanced pair algorithm’, in view of recent progress on the Strong Coincidence Conjecture made by Barge and Diamond.

Type
Research Article
Copyright
2003 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)