On the eigenvalues of finite rank Bratteli–Vershik dynamical systems

DOI10.1017/S0143385709000236zbMath1204.37008arXiv1208.3348OpenAlexW2110145935MaRDI QIDQ3569982

Xavier Bressaud, Alejandro Maass, Fabien Durand

Publication date: 22 June 2010

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.3348

zbMATH Keywords

dynamical systemseigenvaluesBratelli-Vershik diagram

Mathematics Subject Classification ID

Dynamical systems and their relations with probability theory and stochastic processes (37A50) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

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Tower systems for linearly repetitive Delone sets ⋮ Orbit equivalence of Cantor minimal systems and their continuous spectra ⋮ Maximal pronilfactors and a topological Wiener-Wintner theorem ⋮ Torsion-free $S$-adic shifts and their spectrum ⋮ Dynamical properties of minimal Ferenczi subshifts ⋮ Conjugacy of unimodular Pisot substitution subshifts to domain exchanges ⋮ Groups and dynamics: topology, measure, and Borel structure. Abstracts from the workshop held January 16--22, 2022 ⋮ Eigenvalues and strong orbit equivalence ⋮ Eigenvalues of minimal Cantor systems ⋮ Spectral structures and topological methods in mathematical quasicrystals. Abstracts from the workshop held October 1--7, 2017 ⋮ The logarithmic Sarnak conjecture for ergodic weights ⋮ Complexity of nilsystems and systems lacking nilfactors ⋮ Weak mixing directions in non-arithmetic Veech surfaces ⋮ Eigenvalues of Toeplitz minimal systems of finite topological rank ⋮ Finite rank Bratteli diagrams: Structure of invariant measures ⋮ Interplay between finite topological rank minimal Cantor systems, 𝒮-adic subshifts and their complexity

Cites Work

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• Valeurs propres des systèmes dynamiques définis par des substitutions de longueur variable
• Bratteli-Vershik models for Cantor minimal systems associated to interval exchange transformations
• CONTINUOUS AND MEASURABLE EIGENFUNCTIONS OF LINEARLY RECURRENT DYNAMICAL CANTOR SYSTEMS
• Linearly recurrent subshifts have a finite number of non-periodic subshift factors
• ORDERED BRATTELI DIAGRAMS, DIMENSION GROUPS AND TOPOLOGICAL DYNAMICS
• Bratteli–Vershik models for Cantor minimal systems: applications to Toeplitz flows
• NECESSARY AND SUFFICIENT CONDITIONS TO BE AN EIGENVALUE FOR LINEARLY RECURRENT DYNAMICAL CANTOR SYSTEMS

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