Stochastic web as a generator of three-dimensional quasicrystal symmetry |
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Authors: | Zaslavsky G M Edelman M |
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Affiliation: | Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, New York 10012, USA. |
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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. |
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