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arXiv · 1209.3397

On asymptotic description of passage through a resonance in quasi-linear Hamiltonian systems

Anatoly Neishtadt·Tan Su
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Abstract

We consider a quasi-linear Hamiltonian system with one and a half degrees of freedom. The Hamiltonian of this system differs by a small, $\sim\varepsilon$, 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 $\varepsilon$. We provide asymptotic formulas that describe effects of passage through a resonance with an accuracy $O(\varepsilon^{\frac32})$. 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.

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Anatoly Neishtadt, Tan Su. 2012-09-15. On asymptotic description of passage through a resonance in quasi-linear Hamiltonian systems. https://arxiv.org/abs/1209.3397

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