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 iso-energetic non-degeneracy 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⩾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.

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