One-dimensional Substitution Tilings with an Interval Projection Structure

Details One-dimensional Substitution Tilings with an Interval Projection Structure One-dimensional Substitution Tilings with an Interval Projection Structure

2006-01-09

arxiv.org/abs/math/0601187v1

Mathematics

Dynamical Systems

Scientific paper

We 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).

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