The cohomological equation over dynamical systems arising from Delone sets

Daniel Coronel

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)807-833
Number of pages27
JournalErgodic Theory and Dynamical Systems
Issue number3
Publication statusPublished - Jun 2011

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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