Hierarchical structures in Sturmian dynamical systems

  • Authors:
  • Daniel Lenz

  • Affiliations:
  • Fachbereich Mathematik, Johann Wolfgang Coethe-Universität, 60054 Frankfurt, Germany

  • Venue:
  • Theoretical Computer Science - Special issue: Tilings of the plane
  • Year:
  • 2003

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Abstract

The paper is concerned with hierarchical stuctures in subshifis over a finite alphabet. In particular, we present a hierarchy-based approach to Sturmian systems. This approach is then used to characterize the linearly repetitive Sturmian systems (among the Sturmian systems) by uniform positivity of certain weights. More generally, we discuss various bounds on weights and their relationship.Finally, we combine hierarchies and bounds on a weights to study a thermodynamic formalism for lattice gas models associated to arbitrary linearly repetitive subshifts.