Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-14T07:20:44.965Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)