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Journal of the London Mathematical Society (2)

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NECESSARY AND SUFFICIENT CONDITIONS TO BE AN EIGENVALUE FOR LINEARLY RECURRENT DYNAMICAL CANTOR SYSTEMS
XAVIER BRESSAUD, FABIEN DURAND, ALEJANDRO MAASS
Journal:

Journal of the London Mathematical Society / Volume 72 / Issue 3 / December 2005

Published online by Cambridge University Press:

08 December 2005, pp. 799-816

Print publication:

December 2005
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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.

CONTINUOUS AND MEASURABLE EIGENFUNCTIONS OF LINEARLY RECURRENT DYNAMICAL CANTOR SYSTEMS
MARIA ISABEL CORTEZ, FABIEN DURAND, BERNARD HOST, ALEJANDRO MAASS
Journal:

Journal of the London Mathematical Society / Volume 67 / Issue 3 / June 2003

Published online by Cambridge University Press:

20 May 2003, pp. 790-804

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June 2003
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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.