Hierarchical structures in Sturmian dynamical systems

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dc.creatorLenz, Daniel
dc.date2000-05-06
dc.date2000-12-29
dc.date.accessioned2026-07-07T04:35:03Z
dc.date.available2026-07-07T04:35:03Z
dc.descriptionPaper withdrawn; will be replaced by revised version containing application to lattice models as well. We study hierarchical properties of Sturmian words. These properties are similar to those of substitution dynamical systems. This approach allows one to carry over to Sturmian dynamical systems methods developed in the context of substitutions. For example, it allows for a very simple proof of a uniform ergodic type theorem for additive functions taking values in a Banach space. We then focus on establishing various versions of uniform subadditive ergodic type theorems. The main result states that linear repetitivity of a Sturmian system is equivalent to the validity of a uniform subadditive ergodic theorem which in turn is equivalent to uniform positivity of certain weights. Thus, the results of this paper completely cover the validity of uniform additive and subadditive ergodic theorems on Sturmian systems.
dc.descriptionPaper withdrawn; will be replaced by revised version containing application to lattice models
dc.identifierhttps://arxiv.org/abs/math/0005061
dc.identifierhttp://arxiv.org/abs/math/0005061
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59137
dc.subjectDynamical Systems
dc.subjectMathematical Physics
dc.subject34C35, 68R15
dc.titleHierarchical structures in Sturmian dynamical systems
dc.typetext

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