Issues

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1988

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October

  

Reviews of topical problems


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.

Fulltext pdf (1.2 MB)
Fulltext is also available at DOI: 10.1070/PU1988v031n10ABEH005632
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)
BibTex BibNote ® (generic)BibNote ® (RIS)MedlineRefWorks
%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

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