Anna Litvak-Hinenzon, Vered Rom-Kedar 
Parabolic resonances in 3 d.o.f. near integrable Hamiltonian systems
(14624K, Zipped Postscript)

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.