One-dimensional Substitution Tilings with an Interval Projection Structure

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dc.creatorHarriss, Edmund O.
dc.creatorLamb, Jeroen S. W.
dc.date2006-01-09
dc.date.accessioned2026-07-07T06:58:40Z
dc.date.available2026-07-07T06:58:40Z
dc.descriptionWe study nonperiodic tilings of the line obtained by a projection method with an interval projection structure. We obtain a geometric characterisation of all interval projection tilings that admit substitution rules and describe the set of substitution rules for each such a tiling. We show that each substitution tiling admits a countably infinite number of nonequivalent substitution rules. We also provide a complete description of all tilings of the line and half line with an interval projection structure that are fixed by a substitution rule. Finally, we discuss how our results relate to renormalization properties of interval exchange transformations (with two or three intervals).
dc.identifierhttps://arxiv.org/abs/math/0601187
dc.identifierhttp://arxiv.org/abs/math/0601187
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/107450
dc.subjectDynamical Systems
dc.subject52C23; 37E05; 37B50
dc.titleOne-dimensional Substitution Tilings with an Interval Projection Structure
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