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Finite beta-expansions

Published online by Cambridge University Press:  19 September 2008

Christiane Frougny  and
Boris Solomyak
Christiane Frougny
Affiliation:
Université Paris 8 and Laboratoire Informatique Théorique et Programmation, Institut Blaise Pascal, 4 place Jussieu, 75252 Paris Cedex 05, France
Boris Solomyak
Affiliation:
Department of Mathematics GN-50, University of Washington, Seattle, Washington 98195, USA
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Abstract

We characterize numbers having finite β-expansions where β belongs to a certain class of Pisot numbers: when the β-expansion of 1 is equal to a1a2…am, where a1≥a2≥…≥am≥1 and when the β-expansion of 1 is equal to t1t2…tm(tm+1)ω where t1≥t2≥…≥tm>tm+1≥1.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 4 , December 1992 , pp. 713 - 723
Copyright
Copyright © Cambridge University Press 1992

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