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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
Affiliation:
Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170/3 correo 3, Santiago [email protected]
FABIEN DURAND
Affiliation:
Laboratoire Amiénois de, Mathématiques Fondamentales et, Appliquées, CNRS-UMR 6140, Université de Picardie Jules Verne, 33 rue Saint Leu, 80000 Amiens, [email protected]
BERNARD HOST
Affiliation:
Équipe d'Analyse et Mathématiques, Appliquées, CNRS-UMR 8050, Université de Marne-la-Vallée, 93166 Noisy-le-Grand, [email protected]
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, [email protected]
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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.

Type
Research Article
Copyright
The London Mathematical Society 2003

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