Two-symbol Pisot substitutions have pure discrete spectrum

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.

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Bibliographic Details
Published inErgodic theory and dynamical systems Vol. 23; no. 2; pp. 533 - 540
Main Authors HOLLANDER, MICHAEL, SOLOMYAK, BORIS
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.04.2003
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Summary: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.
Bibliography:PII:S0143385702001384
istex:46B8C6014C8575188D9044D67CE3B305431EA1F1
ark:/67375/6GQ-8JMHGXMR-N
ISSN:0143-3857
1469-4417
DOI:10.1017/S0143385702001384