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arXiv · 1811.04654

A new relation between geometric and dynamical properties of objects such as tilings and Delone sets

Yasushi Nagai
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Abstract

Let P be an object such as tiling, Delone set and weighted Dirac comb. There corresponds a dynamical system to P, called the corresponding dynamical system. Such dynamical systems are geometric analogues of symbolic dynamics. It is well-known that there are correspondences between geometric properties of P and properties of the corresponding dynamical system. In this article we give a new correspondence. In other words, we characterize the property that the group of topological eigenvalues for the corresponding dynamical system is not discrete, in terms of a geometric property of P.

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Yasushi Nagai. 2018-11-12. A new relation between geometric and dynamical properties of objects such as tilings and Delone sets. https://arxiv.org/abs/1811.04654

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