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arXiv · 1711.01498

Pisot substitution sequences, one dimensional cut-and-project sets and bounded remainder sets with fractal boundary

Dirk Frettlöh·Alexey Garber
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Abstract

This paper uses a connection between bounded remainder sets in $\mathbb{R}^d$ and cut-and-project sets in $\mathbb{R}$ together with the fact that each one-dimensional Pisot substitution sequence is bounded distance equivalent to some lattice in order to construct several bounded remainder sets with fractal boundary. Moreover it is shown that there are cut-and-project sets being not bounded distance equivalent to each other even if they are locally indistinguishable, more precisely: even if they are contained in the same hull.

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Dirk Frettlöh, Alexey Garber. 2017-11-04. Pisot substitution sequences, one dimensional cut-and-project sets and bounded remainder sets with fractal boundary. https://doi.org/10.1016/j.indag.2018.05.012

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