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22 October 2021
 
  » arxiv » 1209.3397

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On asymptotic description of passage through a resonance in quasi-linear Hamiltonian systems
Anatoly Neishtadt ; Tan Su ;
Date 15 Sep 2012
AbstractWe consider a quasi-linear Hamiltonian system with one and a half degrees of freedom. The Hamiltonian of this system differs by a small, ~epsilon, perturbing term from the Hamiltonian of a linear oscillatory system. We consider passage through a resonance: the frequency of the latter system slowly changes with time and passes through 0. The speed of this passage is of order of epsilon. We provide asymptotic formulas that describe effects of passage through a resonance with an accuracy O(epsilon^(3/2)). This is an improvement of known results by Chirikov (1959), Kevorkian (1971, 1974) and Bosley (1996). The problem under consideration is a model problem that describes passage through an isolated resonance in multi-frequency quasi-linear Hamiltonian systems.
Source arXiv, 1209.3397
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