Chaotic Delone sets

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URI: http://hdl.handle.net/10347/32288
DOI: 10.3934/dcds.2021016

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2021-08

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American Institute of Mathematical Sciences
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Abstract

We present a definition of chaotic Delone set and establish the genericity of chaos in the space of $(\epsilon,\delta)$-Delone sets for $\epsilon\ge\delta$. We also present a hyperbolic analog of the cut-and-project method that naturally produces examples of chaotic Delone sets.

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This article has been published in a revised form in Discrete and Continuous Dynamical Systems [http://dx.doi.org/10.3934/dcds.2021016]. This version is free to download for private research and study only. Not for redistribution, re-sale or use in derivative works.

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Delone set| chaos| tiling| foliated space| hyperbolic dynamical system| geodesic flow

Bibliographic citation

Álvarez López, J.A., Barral Lijó, R., Hunton, J., Nozawa, H., Parker, J.R. (2021). Chaotic Delone sets, "Discrete Contin. Dyn. Syst.", vol. 41, 3781-3796.

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FEDER/Ministerio de Ciencia, Innovación y Universidades/AEI/MTM2017-89686-P [A.L., B.L., H.N.]; Xunta de Galicia/ED431C 2019/10 [A.L., B.L., H.N.]; JSPS Grant-in-Aid for Scientific Research 17K14195 [H.N]; Canon Foundation in Europe Research Fellowship [B.L].

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Attribution-NonCommercial-NoDerivatives 4.0 Internacional

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