- 00-92 Anna Litvak-Hinenzon, Vered Rom-Kedar
- Parabolic resonances in near integrable Hamiltonian systems
(3013K, Gzipped PostScript, Latex2e)
Feb 29, 00
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Abstract. When an integrable Hamiltonian system, possessing an $m$-resonant lower
dimensional normally parabolic torus is perturbed, a parabolic $m$-resonance
occurs. If, in addition, the isoenergetic nondegeneracy condition
for the integrable system fails, the near integrable Hamiltonian
exhibits a flat parabolic $m$-resonance.
It is established that most kinds of parabolic
resonances are persistent in $n$ ($n\geq 3$) d.o.f. near integrable
Hamiltonians, without the use of external parameters. Analytical and
numerical study of a
phenomenological model of a 3 degrees of freedom (d.o.f.) near integrable
Hamiltonian system reveals that in 3 d.o.f. systems new
types of parabolic resonances appear. Numerical
study suggests that some of them cause instabilities in
several directions of the phase space and a new type of
complicated chaotic behavior.
A model describing weather balloons motion
exhibits the same dynamical behavior as the phenomenological model.