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Two-symbol Pisot substitutions have pure discrete spectrum

Published online by Cambridge University Press:  22 September 2003

MICHAEL HOLLANDER and
BORIS SOLOMYAK
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)
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Abstract

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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.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 2 , April 2003, pp. 533 - 540
Copyright
2003 Cambridge University Press