Dynamical properties of almost repetitive Delone sets

Frettlöh D, Richard C (2014)

Publication Type: Journal article

Publication year: 2014


Publisher: American Institute of Mathematical Sciences (AIMS)

Book Volume: 34

Pages Range: 531-556

Journal Issue: 2

DOI: 10.3934/dcds.2014.34.531


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.

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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


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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