- 00-456 Anna Litvak-Hinenzon, Vered Rom-Kedar
- Parabolic resonances in 3 d.o.f. near integrable Hamiltonian systems
(14624K, Zipped Postscript)
Nov 14, 00
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Abstract. When an integrable 3 degrees of freedom (d.o.f.) Hamiltonian system,
possessing an m-resonant (m=1 or 2) normally parabolic torus is
perturbed, a parabolic m-resonance occurs. Parabolic 1-resonances are
persistent (without the use of external parameters)
in near integrable n (n >= 3) d.o.f. Hamiltonians.
Other types of parabolic resonances are persistent in this
class of systems as a low (one or two) co-dimension phenomena, and thus they
are expected to appear in many applications. Analytical and numerical study of
a phenomenological model containing parabolic resonances of various types
reveals the differences between the dynamics appearing in 2 and 3 d.o.f.
systems. The energy-momenta bifurcation diagram is developed as a tool for
studying the global structure of such systems. The numerical study
demonstrates that parabolic resonances are an unavoidable source of large and
fast instabilities in typical 3 d.o.f. systems.