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.

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