Dynamical properties of almost repetitive Delone sets

Frettlöh D, Richard C (2014)

Publication Type: Journal article

Publication year: 2014

Journal

Discrete and Continuous Dynamical Systems American Institute of Mathematical Sciences (AIMS)

Publisher: American Institute of Mathematical Sciences (AIMS)

Book Volume: 34

Pages Range: 531-556

Journal Issue: 2

DOI: 10.3934/dcds.2014.34.531

Abstract

We consider the collection of uniformly discrete point sets in Euclidean space equipped with the vague topology. For a point set in this collection, we characterise minimality of an associated dynamical system by almost repetitivity of the point set. We also provide linear versions of almost repetitivity which lead to uniquely ergodic systems. Apart from linearly repetitive point sets, examples are given by periodic point sets with almost periodic modulations, and by point sets derived from primitive substitution tilings of finite local complexity with respect to the Euclidean group with dense tile orientations.

Authors with CRIS profile

Christoph Richard Lehrstuhl für Mathematische Stochastik

Involved external institutions

Universität Bielefeld DE Germany (DE)

How to cite

APA:

Frettlöh, D., & Richard, C. (2014). Dynamical properties of almost repetitive Delone sets. Discrete and Continuous Dynamical Systems, 34(2), 531-556. https://dx.doi.org/10.3934/dcds.2014.34.531

MLA:

Frettlöh, Dirk, and Christoph Richard. "Dynamical properties of almost repetitive Delone sets." Discrete and Continuous Dynamical Systems 34.2 (2014): 531-556.

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