Continuous and Measurable Eigenfunctions of Linearly Recurrent Dynamical Cantor Systems
By María Isabel Cortez, Fabien Durand, B. Host, Alejandro Maass. 2003
48 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/23d23083b70da723d979307349f7a590d776bc82
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In Computational Theory and Mathematics
- S. Bezuglyi
- J. Kwiatkowski
- Boris Solomyak
- Konstantin Medynets
- Val'erie Berth'e
- Vincent Delecroix
- Pablo Shmerkin
In Mathematical Physics
- S. Bezuglyi
- J. Kwiatkowski
- Boris Solomyak
- Val'erie Berth'e
- Vincent Delecroix
- Konstantin Medynets
- Pablo Shmerkin
- Jonathan M. Fraser
Citations in the corpus
- Finite rank Bratteli diagrams: Structure of invariant measures (2010, background): “ES81]. The choice of finite rank systems is based on their “relative” combinatorial simplicity and, at the same time, on the intriguing properties and non-trivial dynamical behavior, see, for example, [CDHM03], [BDM10], [D10, Chapter 6], and [BKMS10]. We observethat substitution dynamical systems, mi”
- Beyond substitutive dynamical systems: S-adic expansions (2013, background): “For linearly re‐ current systems, topological and measurable eigenvalues are completely characterized [57, 47, 48].”