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Lagrangian tori near resonances of near-integrable Hamiltonian systems | | Anton Medvedev
; Anatoly Neishtadt
; Dmitry Treschev
; | | Date: |
1 Nov 2013 | | Abstract: | In this paper we study families of Lagrangian tori that appear in a
neighborhood of a resonance of a near-integrable Hamiltonian system. Such
families disappear in the "integrable" limit $varepsilon o 0$. Dynamics on
these tori is oscillatory in the direction of the resonance phases and rotating
with respect to the other (non-resonant) phases.
We also show that, if multiplicity of the resonance equals one, generically
these tori occupy a set of large relative measure in the resonant domains in
the sense that the relative measure of the remaining "chaotic" set is of order
$sqrtvarepsilon$. Therefore for small $varepsilon > 0$ a random initial
condition in a $sqrtvarepsilon$-neighborhood of a single resonance occurs
inside this set (and therefore generates a quasi-periodic motion) with a
probability much larger than in the "chaotic" set.
We present results of numerical simulations and discuss the form of
projection of such tori to the action space. | | Source: | arXiv, 1311.0132 | | Services: | Forum | Review | PDF | Favorites | |
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