Abstract
We are engaged in classifying up to isomorphism of discrete subgroups of an affine transformation group on a plane (a two-dimensional space) preserving the Minkowski metric. It is proved that, for subgroups that do not coincide with Euclidean ones, the orbit of almost every point is everywhere dense.
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REFERENCES
R. M. Garipov, “An algebraic method for computing crystallographic groups I, ” Sib. Zh. Ind. Mat., 3, No. 2, 43–62 (2000).
R. M. Garipov, “An algebraic method for computing crystallographic groups II, ” Sib. Zh. Ind. Mat., 4, No. 1, 52–72 (2001).
I. A. Baltag and V. P. Garit, “A complete description of Fyodorov groups on a pseudoeuclidean space, ” in Inquiries in Discrete Geometry, KSU, Kishinev (1974), pp. 91–107.
I. A. Baltag and V. P. Garit, Two-Dimensional Discrete Affine Groups [in Russian], Stiinca, Kishinev (1981).
L. Bieberbach, “Ñber die Bewegungsgruppen der Euklidischen Räume, ” Math. Ann., 70, 297–336 (1911).
L. Bieberbach, “Die Gruppen mit endlichem Fundamentalbereich, ” Math. Ann., 72, 400–412 (1912).
B. Delone, N. Padurov, and A. Aleksandrov, Mathematical Foundations in the Structural Analysis of Crystals [in Russian], Gostekhizdat, Moscow (1934).
K. F. Gauss, Memoirs in Number Theory [Russian translation], AN SSSR, Moscow (1959).
P. Billingsley, Ergodic Theory and Information, Wiley, New York (1965).
B. M. Gurevich and Ya. G. Sinai, “Algebraic automorphisms of tori and the Markov chain, ” Suppl. [9], pp. 205–233.
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Garipov, R.M. Ornament Groups on a Minkowski Plane. Algebra and Logic 42, 365–381 (2003). https://doi.org/10.1023/B:ALLO.0000004170.97211.21
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DOI: https://doi.org/10.1023/B:ALLO.0000004170.97211.21