Stochastic web as a generator of three-dimensional quasicrystal symmetry

Abstract

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.

Stochastic webs and quantum transport in superlattices: an introductory review

“…We shall review just three of the more important of them, concentrating on the model of a harmonic oscillator subject to a plane wave, which will be relevant to our discussion of semiconductor SLs below. A good review of a broad range of the early work on low-dimensional stochastic webs may be found in [1]; more recent work is reviewed in [26] (see also [17]).…”

Properties of quasiperiodic functions

“…Recently a new field has appeared: the behavior of cold atoms in a quasi periodic poten tial [28][29][30][31]. Closely related is the study of stochastic webs, here the quasiperiodic functions represent the Hamiltonian [32][33][34][35][36][37][38][39]. Quasiperiodic function also show up directly or indirectly in all kinds of soft matter modeling approaches [40][41][42][43][44][45].…”