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Continuous and Measurable Eigenfunctions of Linearly Recurrent Dynamical Cantor Systems
Author(s) -
Cortez Maria Isabel,
Durand Fabien,
Host Bernard,
Maass Alejandro
Publication year - 2003
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/s0024610703004320
Subject(s) - mathematics , rigidity (electromagnetism) , dynamical systems theory , class (philosophy) , pure mathematics , eigenvalues and eigenvectors , measure (data warehouse) , cantor set , eigenfunction , property (philosophy) , dynamical system (definition) , mathematical analysis , discrete mathematics , physics , quantum mechanics , computer science , philosophy , epistemology , database , artificial intelligence
The class of linearly recurrent Cantor systems contains the substitution subshifts and some odometers. For substitutionsubshifts, measure‐theoretical and continuous eigenvalues are the same. It is natural to ask whether this rigidity property remains true for the class of linearly recurrent Cantor systems. Partial answers are given to this question.