A classification of the point spectrum of constant length substitution tiling spaces and general fixed point theorems for tilings

2016-03-11T16:11:58Z (GMT) by Dina Asaad Abuzaid
We examine the point spectrum of the various tiling spaces that result from different choices of tile lengths for substitution of constant length on a two or a three letter alphabet. In some cases we establish insensitivity to changes in length. In a wide range of cases, we establish that the typical choice of length leads to trivial point spectrum. We also consider a problem related to tilings of the integers and their connection to fixed point theorems. Using this connection, we prove a generalization of the Banach Contraction Principle.

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