Minimal chaos, stochastic webs, and structures of quasicrystal symmetry

The relationship between the problem of the symmetry of a plane tiling and the properties of nonintegrable dynamic systems is reviewed. The formation of stochastic layers and a stochastic web in the motion of linear and nonlinear oscillators subjected to a perturbation is discussed in detail. Emphasis is placed on research on the symmetry properties of a stochastic web with a fractal structure of a quasicrystal type. Structures with a quasicrystal symmetry form as a result of an interaction of two types of symmetries: translational and rotational. Various characteristics of structures with a quasicrystal symmetry are discussed: the distributions of stable and unstable points, the state density, and the Fourier spectrum. Quasicrystal structures in solid state physics, hydrodynamics, botany, and ornamental art are discussed.

PACS: 61.44.Br, 05.45.Df (all)
DOI: 10.1070/PU1988v031n10ABEH005632
URL: https://ufn.ru/en/articles/1988/10/a/
Citation: Zaslavskii G M, Sagdeev R Z, Usikov D A, Chernikov A A "Minimal chaos, stochastic webs, and structures of quasicrystal symmetry" Sov. Phys. Usp. 31 887–915 (1988)

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%0 Journal Article
%T Minimal chaos, stochastic webs, and structures of quasicrystal symmetry
%A G. M. Zaslavskii
%A R. Z. Sagdeev
%A D. A. Usikov
%A A. A. Chernikov
%I Physics-Uspekhi
%D 1988
%J Phys. Usp.
%V 31
%N 10
%P 887-915
%U https://ufn.ru/en/articles/1988/10/a/
%U https://doi.org/10.1070/PU1988v031n10ABEH005632

Оригинал: Заславский Г М, Сагдеев Р З, Усиков Д А, Черников А А «Минимальный хаос, стохастическая паутина и структуры с симметрией типа „квазикристалл“» УФН 156 193–251 (1988); DOI: 10.3367/UFNr.0156.198810a.0193