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

2018/11/12 by Nagai, Yasushi
#37B50 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1811.04654

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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