Nonlinear Phenomena in Complex Systems, 2021, Vol.24, No.2, pp.156

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2021, Vol.24, No.2, pp.156 - 165

Structurally Stable Symmetric Tilings on the Plane

Maria V. Makarova, Ivan A. Kovalew and Dmitry W. Serow

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.

Key words: dynamic system, m-fold symmetry, quasicrystal, self-similarity, pentagonal tiling, heptagonal tiling, quasi-periodic function, Schnirelmann density, additive basis, order of basis, fractional density, PostScript

DOI: https://doi.org/10.33581/1561-4085-2021-24-2-156-165

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