Diffusion and drift in volume-preserving maps View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2017-11

AUTHORS

Nathan Guillery, James D. Meiss

ABSTRACT

A nearly-integrable dynamical system has a natural formulation in terms of actions, y (nearly constant), and angles, x (nearly rigidly rotating with frequency Ω(y)).We study angleaction maps that are close to symplectic and have a twist, the derivative of the frequency map, DΩ(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 Froeschl´e map in four-dimensions shows that this theory gives accurate results for the rank-one case. More... »

PAGES

700-720

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1134/s1560354717060089

DOI

http://dx.doi.org/10.1134/s1560354717060089

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https://app.dimensions.ai/details/publication/pub.1099694866


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