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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 | | 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, ~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 | | Services: | Forum | Review | PDF | Favorites | |
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