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CONTINUOUS AND MEASURABLE EIGENFUNCTIONS OF LINEARLY RECURRENT DYNAMICAL CANTOR SYSTEMS

Published online by Cambridge University Press:  20 May 2003

MARIA ISABEL CORTEZ ,
FABIEN DURAND ,
BERNARD HOST  and
ALEJANDRO MAASS
MARIA ISABEL CORTEZ
Affiliation:
Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170/3 correo 3, Santiago Chilemcortez@dim.uchile.cl
FABIEN DURAND
Affiliation:
Laboratoire Amiénois de, Mathématiques Fondamentales et, Appliquées, CNRS-UMR 6140, Université de Picardie Jules Verne, 33 rue Saint Leu, 80000 Amiens, Francefdurand@u-picardie.fr
BERNARD HOST
Affiliation:
Équipe d'Analyse et Mathématiques, Appliquées, CNRS-UMR 8050, Université de Marne-la-Vallée, 93166 Noisy-le-Grand, Francehost@math.univ-mlv.fr
ALEJANDRO MAASS
Affiliation:
Departamento de Ingeniería Matemática, Universidad de Chile, and Centro de Modelamiento Matemático, UMR 2071 UCHILE-CNRS, Casilla 170/3 correo 3, Santiago, Chileamaass@dim.uchile.cl
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Abstract

The class of linearly recurrent Cantor systems contains the substitution subshifts and some odometers. For substitutionsubshifts, measure-theoretical and continuous eigenvalues are the same. It is natural to ask whether this rigidity property remains true for the class of linearly recurrent Cantor systems. Partial answers are given to this question.

Keywords

54H20 (primary)37B20 (secondary)
Type
Research Article
Information
Journal of the London Mathematical Society , Volume 67 , Issue 3 , June 2003 , pp. 790 - 804
Copyright
The London Mathematical Society 2003

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