Symmetry and chaos
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.
scientific article; zbMATH DE number 4157399