Substitution dynamical systems : algebraic characterization of eigenvalues

DOI10.24033/asens.1746zbMath0866.11023OpenAlexW2188717226MaRDI QIDQ4717348

Arnaldo Nogueira, Sébastien Ferenczi, Christian Mauduit

Publication date: 20 July 1997

Published in: Annales scientifiques de l'École normale supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_1996_4_29_4_519_0

zbMATH Keywords

Pisot numbersautomatic sequencesweakly mixingprimitive substitutioneigenvalues of dynamical systems

Mathematics Subject Classification ID

Automata sequences (11B85) Low-dimensional dynamical systems (37E99)

Related Items (19)

How to prove that a sequence is not automatic ⋮ Dynamical directions in numeration ⋮ Pure discrete spectrum dynamical system and periodic tiling associated with a substitution ⋮ A connection between palindromic and factor complexity using return words ⋮ Self-induced systems ⋮ Episturmian words: a survey ⋮ Topological mixing notions on Turing machine dynamical systems ⋮ Spectral characteristics of Schrödinger operators generated by product systems ⋮ Self-similarity and spectral theory: on the spectrum of substitutions ⋮ Rotated odometers ⋮ Conjugacy of unimodular Pisot substitution subshifts to domain exchanges ⋮ Uniformly distributed orbits in \(\mathbb{T}^d\) and singular substitution dynamical systems ⋮ The Cech cohomology and the spectrum for 1-dimensional tiling systems ⋮ On ergodic averages for parabolic product flows ⋮ On the modulus of continuity for spectral measures in substitution dynamics ⋮ Eigenvalues of minimal Cantor systems ⋮ Graph towers, laminations and their invariant measures ⋮ Sequences with constant number of return words ⋮ Weak mixing in interval exchange transformations of periodic type

Cites Work

• A sufficient condition for weak mixing of subtitutions and stationary adic transformations
• Substitution dynamical systems - spectral analysis
• Caractérisation des ensembles normaux substitutifs. (Characterization of normal substitutional sets)
• Gauss measures for transformations on the space of interval exchange maps
• Valeurs propres des systèmes dynamiques définis par des substitutions de longueur variable
• The spectrum of dynamical systems arising from substitutions of constant length
• Topological weak-mixing of interval exchange maps
• Interval exchange transformations
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