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Dynamics for β-shifts and Diophantine approximation

Published online by Cambridge University Press:  01 December 2007

BORIS ADAMCZEWSKI  and
YANN BUGEAUD
BORIS ADAMCZEWSKI
Affiliation:
CNRS, Université de Lyon, Université Lyon 1, Institut Camille Jordan, 21 avenue Claude Bernard, 69622 Villeurbanne Cedex, France (email: [email protected])
YANN BUGEAUD
Affiliation:
Université Louis Pasteur, U. F. R. de mathématiques, 7, rue René Descartes, 67084 Strasbourg Cedex, France (email: [email protected])
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Abstract

We investigate the β-expansion of an algebraic number in an algebraic base β. Using tools from Diophantine approximation, we prove several results that may suggest a strong difference between the asymptotic behaviour of eventually periodic expansions and that of non-eventually periodic expansions.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 6 , December 2007 , pp. 1695 - 1711
Copyright
Copyright © Cambridge University Press 2007

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