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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.