The cohomological equation over dynamical systems arising from Delone sets

Daniel Coronel

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

2 Citas (Scopus)

Resumen

The hull Ω of an aperiodic repetitive Delone set P in ℝd is a compact metric space on which ℝd acts continuously by translation. Let G be ℝm or Tm and α be a continuous G-cocycle over the dynamical system (Ω, ℝd). In this paper we study conditions under which the cohomological equation α(ω, x)= ψ(ω-x)-ψ(ω) has continuous solutions. We give a sufficient condition for general continuous G-cocycles and a necessary condition for transversally locally constant G-cocycles. These conditions are given in terms of the set of first return vectors associated with a tower system for Ω. For linearly repetitive Delone sets we give a necessary and sufficient condition for solving the cohomological equation in the class of transversally Hölder G-cocycles.

Idioma originalInglés
Páginas (desde-hasta)807-833
Número de páginas27
PublicaciónErgodic Theory and Dynamical Systems
Volumen31
N.º3
DOI
EstadoPublicada - jun 2011

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