Necessary and Sufficient Conditions to be Aneigenvalue for Linearly Recurrent Dynamical Cantor Systems

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2005-12
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Necessary and Sufficient Conditions to be Aneigenvalue for Linearly Recurrent Dynamical Cantor Systems
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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.
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Programa Iniciativa Científica Milenio P01-005 and FONDECYT 1010447. This project was also partially supported by the international cooperation programme ECOS-CONICYT C03-E03 and FONDECYT for international cooperation agreement 7040166.
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ISSN: 0024-6107
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JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, V.: 72, p.: 799-816, Part 3, DEC 2005
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