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Эта публикация цитируется в 13 научных статьях (всего в 13 статьях)
Diffusion and Drift in Volume-Preserving Maps
Nathan Guillery, James D. Meiss Department of Applied Mathematics, University of Colorado Boulder, Boulder, CO 80309-0526
Аннотация:
A nearly-integrable dynamical system has a natural formulation in terms of actions, $y$ (nearly constant), and angles, $x$ (nearly rigidly rotating with frequency $\Omega(y)$).
We study angle-action maps that are close to symplectic and have a twist, the derivative of the frequency map, $D\Omega(y)$, that is positive-definite. When the map is symplectic,
Nekhoroshev's theorem implies that the actions are confined for exponentially long times: the drift is exponentially small and numerically appears to be diffusive. We show that when
the symplectic condition is relaxed, but the map is still volume-preserving, the actions can have a strong drift along resonance channels. Averaging theory is used to compute the
drift for the case of rank-$r$ resonances. A comparison with computations for a generalized Froeschlé map in four-dimensions shows that this theory gives accurate results for
the rank-one case.
Ключевые слова:
symplectic maps, Nekhoroshev’s theorem, chaotic transport.
Поступила в редакцию: 13.09.2017 Принята в печать: 18.10.2017
Образец цитирования:
Nathan Guillery, James D. Meiss, “Diffusion and Drift in Volume-Preserving Maps”, Regul. Chaotic Dyn., 22:6 (2017), 700–720
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd284 https://www.mathnet.ru/rus/rcd/v22/i6/p700
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