Necessary and sufficient conditions to be an eigenvalue for linearly recurrent dynamical Cantor systems

Details Necessary and sufficient conditions to be an eigenvalue for linearly recurrent dynamical Cantor systems Necessary and sufficient conditions to be an eigenvalue for linearly recurrent dynamical Cantor systems

2008-01-30

arxiv.org/abs/0801.4619v1

Journal of the London Mathematical Society 72, 3 (2005) 799-816

Mathematics

Dynamical Systems

18 pages

Scientific paper

We give necessary and sufficient conditions to have measurable and continuous
eigenfunctions for linearly recurrent Cantor dynamical systems. We also
construct explicitly an example of linearly recurrent system with nontrivial
Kronecker factor and a trivial maximal equicontinuous factor.

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