Structurally Stable Symmetric Tilings on the Plane-Reference-Cited by-同舟云学术

Structurally Stable Symmetric Tilings on the Plane

Published:2021-06-25 Issue:2 Volume:24 Page:156-165
ISSN:1817-2458
Container-title:Nonlinear Phenomena in Complex Systems
language:en
Short-container-title:

Author:

Makarova Maria V.¹,Kovalew Ivan A.²,Serow Dmitry W.²

Affiliation:

1. Saint-Petersburg State University of Aerospace Instrumentation

2. Peter the Great St. Petersburg Polytechnic University

Abstract

A symmetric m-tilings model on the plane is assembled to be a phase portrait for a structurally stable Hamiltonian system. Integral of the system is the quasi-periodic function with m-fold rotational symmetry being result of the semi-dynamic system action on the unit interval. Some examples for pentagonal and heptagonal tilings has been built in detail. Some properties of an additive measure and order for tilings have been discussed.

Publisher

Belarusian State University

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Reference34 articles.

1. I. A. Dynnikov, S. P. Novikov. Topology of Quasi-periodic Functions on the Plane. Russian Math. Surveys. 60,1−26 (2005). (in Russian)

2. A. B. Antonevich, A. N. Buzulutskaya (Glaz). Almost-Periodic Algebras and Their Automorphisms. Math. Notes. 102, 610−622 (2017).

3. N. G. Bruijnde. Quasicrystals and their Fourier transform. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Mathematical Sciences. A89,123152 (1986).

4. ́an T. von K ́arm, H. L. Rubach. On the Structurally Stable Symmetric Tilings on the mechanisms of fluid resistance. Physik Z. , 49−59 (1912).

5. H. B ́enard. Les tourbillons cellulaires dans unenappe liquide. Rev. G ́en. Sciences Pure Appl. 11, 1261-1271 (1900); ibid11, 1309−1328 (1900).