Symmetry and chaos
type: Item
instance of: scholarly article
title: Symmetry and chaos
zbMATH Open document ID: 0705.52019
DOI: 10.1016/0898-1221(89)90145-4
author: A. A. Chernikov
author: R. Z. Sagdeev
author: D. A. Usikov
author: George M. Zaslavsky
publication date: 1989-01-01T00:00:00Z
review text: The paper considers the dynamical model of a particle moving in a magnetic field and the field of perpendicular wave packet field. Let K be a parameter proportional to the wave packet amplitude and let \(\alpha =2\pi /q\) be the angle by which the particle turns between two consecutive kicks caused by the wave packet. For certain conditions, the coordinates of the succeeding positions of the particle in the phase plane are given by so called tiling generator: \[ u_{n+1}=(u_ n+K \sin v_ n)\cos \alpha +v_ n\sin \alpha, \] \[ v_{n+1}=-(u_ n+K \sin v_ n)\sin \alpha +v_ n\cos \alpha. \] The walking of the particle generates a tiling of the plane with rotational and translation quasisymmetry. The authors discuss relationships between tilings obtained by tiling generators and tilings in geometry, art and crystallography. There are prospect for computer graphics; the tiling generator is useful for plotting various ornaments.
Mathematics Subject Classification ID: 52C20
Mathematics Subject Classification ID: 78A40
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 68U05
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 82D25
zbMATH DE Number: 4157399
zbMATH Keywords: stochastic web
zbMATH Keywords: magnetic field
zbMATH Keywords: wave packet
zbMATH Keywords: tiling generator
zbMATH Keywords: quasisymmetry
zbMATH Keywords: tilings in geometry
zbMATH Keywords: art
zbMATH Keywords: crystallography
zbMATH Keywords: computer graphics
zbMATH Keywords: ornaments
reviewed by: Marek Lassak
MaRDI profile type: Publication
full work available at URL: 0898-1221(89)90145-4
OpenAlex ID: W1967517280
cites work: Q5534201
cites work: Q3273607
cites work: Q3901467
cites work: Minimal chaos and stochastic webs
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4157399