Rothos V.M., Bountis T.
Mel'nikov's Vector and Singularity Analysis of N DOF Hamiltonian Systems
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ABSTRACT.  We investigate periodically perturbed, integrable 2 degree of freedom (d.o.f.) 
Hamiltonian systems as a paradigm of the dynamics of 3 d.o.f. Hamiltonian      
systems.                                    
We derive the Mel'nikov vector, determining transversal intersections of the   
invariant manifolds of a saddle fixed point of the associated (time-periodic)  
map and investigate its connection with the breakdown of the Painlev\'e        
property of the unperturbed solutions in complex time.