Fractional standard map |
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Authors: | Mark Edelman Vasily E Tarasov |
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Institution: | a Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012, USA b Department of Physics, Stern College at Yeshiva University, 245 Lexington Avenue, New York, NY 10016, USA c Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow 119991, Russia |
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Abstract: | Properties of the phase space of the standard map with memory are investigated. This map was obtained from a kicked fractional differential equation. Depending on the value of the map parameter and the fractional order of the derivative in the original differential equation, this nonlinear dynamical system demonstrates attractors (fixed points, stable periodic trajectories, slow converging and slow diverging trajectories, ballistic trajectories, and fractal-like structures) and/or chaotic trajectories. At least one type of fractal-like sticky attractors in the chaotic sea was observed. |
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Keywords: | 05 45 Pq 45 10 Hj |
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