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NECESSARY AND SUFFICIENT CONDITIONS TO BE AN EIGENVALUE FOR LINEARLY RECURRENT DYNAMICAL CANTOR SYSTEMS

Published online by Cambridge University Press:  08 December 2005

XAVIER BRESSAUD ,
FABIEN DURAND  and
ALEJANDRO MAASS
XAVIER BRESSAUD
Affiliation:
Centro de Modelamiento Matemático, UMR 2071 UCHILE-CNRS, Casilla 170/3 correo 3, Santiago, Chile, Institut de Mathématiques de Luminy, 163 avenue de Luminy, Case 907, 13288 Marseille Cedex 9, Francebressaud@dim.uchile.cl, bressaud@iml.univ-mrs.fr
FABIEN DURAND
Affiliation:
Laboratoire Amiénois de Mathématiques Fondamentales et Appliquées, CNRS-UMR 6140, Université de Picardie Jules Verne, 33 rue Saint Leu, 80000 Amiens, Francefabien.durand@u-picardie.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

Necessary and sufficient conditions are given for linearly recurrent Cantor dynamical systems to have measurable and continuous eigenfunctions. Also an example of a linearly recurrent system with a nontrivial Kronecker factor and a trivial maximal equicontinuous factor is constructed explicitly.

Keywords

54H20 (primary)37B20 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 72 , Issue 3 , December 2005 , pp. 799 - 816
Copyright
The London Mathematical Society 2005

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