Abstract
Linearly repetitive Delone sets are the simplest aperiodic repetitive Delone sets of the Euclidean space, e.g. any self similar Delone set is linearly repetitive.We present here some combinatorial, ergodic and mixing properties of their associated dynamical systems. We also give a characterization of such sets via the patch frequencies. Finally, we explain why a linearly repetitive Delone set is the image of a lattice by a bi-Lipschitz map.
Mathematics Subject Classification (2010). 37B50.
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Aliste-Prieto, J., Coronel, D., Cortez, M.I., Durand, F., Petite, S. (2015). Linearly Repetitive Delone Sets. In: Kellendonk, J., Lenz, D., Savinien, J. (eds) Mathematics of Aperiodic Order. Progress in Mathematics, vol 309. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0903-0_6
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DOI: https://doi.org/10.1007/978-3-0348-0903-0_6
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0902-3
Online ISBN: 978-3-0348-0903-0
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