Abstract:
We survey the results of the local theory of regular systems that are related to estimating the regularity radius. We also discuss recent results on local groups in arbitrary Delone sets in the plane and in the three-dimensional space, including new theorems and conjectures generalizing the classical statement on the absence of fivefold rotations in lattices.
This work was performed at the Steklov International Mathematical Center and supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2022-265).
Citation:
N. P. Dolbilin, “Local Theory of Regular Systems and Delone Sets”, Geometry, Topology, and Mathematical Physics, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 85th birthday, Trudy Mat. Inst. Steklova, 325, Steklov Mathematical Institute of RAS, Moscow, 2024, 129–145; Proc. Steklov Inst. Math., 325 (2024), 120–135
\Bibitem{Dol24}
\by N.~P.~Dolbilin
\paper Local Theory of Regular Systems and Delone Sets
\inbook Geometry, Topology, and Mathematical Physics
\bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 85th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 325
\pages 129--145
\publ Steklov Mathematical Institute of RAS
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4397}
\crossref{https://doi.org/10.4213/tm4397}
\zmath{https://zbmath.org/?q=an:07939065}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 325
\pages 120--135
\crossref{https://doi.org/10.1134/S008154382402007X}
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Citation in format AMSBIB
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