One-dimensional Substitution Tilings with an Interval Projection Structure
动力系统
2007-05-23 v1
摘要
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).
引用
@article{arxiv.math/0601187,
title = {One-dimensional Substitution Tilings with an Interval Projection Structure},
author = {Edmund O. Harriss and Jeroen S. W. Lamb},
journal= {arXiv preprint arXiv:math/0601187},
year = {2007}
}