Necessary and Sufficient Conditions to be an Eigenvalue for Linearly Recurrent Dynamical Cantor Systems | Zendy

Bressaud Xavier | Zendy; Durand Fabien | Zendy; Maass Alejandro | Zendy

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

Author(s) -

Bressaud Xavier,

Durand Fabien,

Maass Alejandro

Publication year - 2005

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/s0024610705006800

Subject(s) - equicontinuity , kronecker delta , mathematics , eigenfunction , eigenvalues and eigenvectors , dynamical systems theory , pure mathematics , linear dynamical system , cantor function , dynamical system (definition) , mathematical analysis , linear system , cantor set , physics , quantum mechanics

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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