Rothos V.M., Bountis T.
MEL'NIKOV ANALYSIS OF PHASE SPACE TRANSPORT IN A N--DEGREE--OF--FREEDOM
HAMILTONIAN SYSTEMS--DISCRETE NLS EQUATION
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ABSTRACT. We study the connections between Mel'nikov 's analysis and phase space transport
in an N--d.o.f Hamiltonian System, associated with a Discrete Nonlinear Schrodinger
Equation (DNLS) with $N+1$ elements. Using the two element system as the
underlying integrable subsystem we treat the coupling to the additional
oscillators perturbatively. The nonintegrability of the DNLS equation with
four elements has been proved by Henning et al. By means of Wiggins 's generalized
Mel'nikov method, we prove nonintegrability in the arbitrary $N$ case through the existence of chaotic
dynamics, study diffusion of orbits in phase space.