Stochastic web as a generator of three-dimensional quasicrystal symmetry.
It is shown that two coupled oscillators perturbed by periodic kicks generate a thin stochastic web in the four-dimensional phase space, which differs from the Arnold web. Under some resonance-type condition the web possesses a quasicrystal-type symmetry. In three-dimensional coordinate space, the web's symmetry corresponds to the icosahedral one and, due to that, the original four-dimensional map can be considered as a dynamical generator of the quasicrystal-type tiling of three-dimensional space.
Zaslavsky
G M
GM
Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, New York 10012, USA.
Edelman
M
M