A new relation between geometric and dynamical properties of objects such as tilings and Delone sets
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 wellknown 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2018
 arXiv:
 arXiv:1811.04654
 Bibcode:
 2018arXiv181104654N
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematical Physics;
 37B50
 EPrint:
 one figure