Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies

Baake M, Lenz D, Richard C (2007)

Publication Type: Journal article

Publication year: 2007

Journal

Letters in Mathematical Physics Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 82

Pages Range: 61-77

Journal Issue: 1

URI: http://link.springer.com/article/10.1007/s11005-007-0186-7

DOI: 10.1007/s11005-007-0186-7

Abstract

Delone sets of finite local complexity in Euclidean space are investigated. We show that such a set has patch counting and topological entropy zero if it has uniform cluster frequencies and is pure point diffractive. We also note that the patch counting entropy vanishes whenever the repetitivity function satisfies a certain growth restriction.

Authors with CRIS profile

Christoph Richard Lehrstuhl für Mathematische Stochastik

Involved external institutions

Universität Bielefeld DE Germany (DE) Technische Universität Chemnitz DE Germany (DE)

How to cite

APA:

Baake, M., Lenz, D., & Richard, C. (2007). Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies. Letters in Mathematical Physics, 82(1), 61-77. https://doi.org/10.1007/s11005-007-0186-7

MLA:

Baake, Michael, Daniel Lenz, and Christoph Richard. "Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies." Letters in Mathematical Physics 82.1 (2007): 61-77.

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