A non-regular Toeplitz flow with preset pure point spectrum

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Title

Authors ¹, ²

Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
U.B.O. Faculté des Sciences et Techniques, Département de Mathématiques, 6 Av. V. Le Gorgeu, B.P. 809, 29287 Brest Cedex, France

Given an arbitrary countable subgroup

σ_{0}

of the torus, containing infinitely many rationals, we construct a strictly ergodic 0-1 Toeplitz flow with pure point spectrum equal to

σ_{0}

. For a large class of Toeplitz flows certain eigenvalues are induced by eigenvalues of the flow Y which can be seen along the aperiodic parts.

Toeplitz sequence, pure point spectrum, strict ergodicity, group extension

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