Translation numbers for a class of maps on the dynamical systems arising from quasicrystals in the real line

DOI10.1017/S0143385709000145zbMath1185.37042MaRDI QIDQ3558040

José Aliste-Prieto

Publication date: 29 April 2010

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

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25)

Related Items

Resonant equilibrium configurations in quasi-periodic media: perturbative expansions ⋮ Homeomorphisms of a solenoid isotopic to the identity and its second cohomology groups ⋮ On the simplicity of homeomorphism groups of a tilable lamination ⋮ Dynamics of induced homeomorphisms of one-dimensional solenoids ⋮ Almost periodic structures and the semiconjugacy problem ⋮ Irrational rotation factors for conservative torus homeomorphisms ⋮ Rotation numbers and rotation classes on one-dimensional tiling spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Substitutions in dynamics, arithmetics and combinatorics
• Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2
• Minimal configurations for the Frenkel-Kontorova model on a quasicrystal
• Spaces of tilings, finite telescopic approximations and gap-labeling
• Linearization of conservative toral homeomorphisms
• The \(C^*\)-algebras associated with minimal homeomorphisms of the Cantor set
• A remark on Schrödinger operators on aperiodic tilings.
• Pure point dynamical and diffraction spectra
• Isomorphism of hierarchical structures
• Rotation Sets for Maps of Tori
• Substitutional dynamical systems, Bratteli diagrams and dimension groups
• Rotation and entropy
• Pattern-equivariant functions and cohomology
• On the dynamics of \mathbb{G} -solenoids. Applications to Delone sets
• Repetitive Delone sets and quasicrystals
• Poincaré rotation number for maps of the real line with almost periodic displacement
• ORDERED BRATTELI DIAGRAMS, DIMENSION GROUPS AND TOPOLOGICAL DYNAMICS
• TOWARDS A CLASSIFICATION FOR QUASIPERIODICALLY FORCED CIRCLE HOMEOMORPHISMS