Dynamics of self-similar tilings

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Abstract

This paper investigates dynamical systems arising from the action by translations on the orbit closures of self-similar and self-affine tilings of ℝd. The main focus is on spectral properties of such systems which are shown to be uniquely ergodic. We establish criteria for weak mixing and pure discrete spectrum for wide classes of such systems. They are applied to a number of examples which include tilings with polygonal and fractal tile boundaries; systems with pure discrete, continuous and mixed spectrum.

Original languageEnglish
Pages (from-to)695-738
Number of pages44
JournalErgodic Theory and Dynamical Systems
Volume17
Issue number3
DOIs
StatePublished - Jun 1997
Externally publishedYes

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