Limiting phase trajectories and resonance energy transfer in a system of two coupled oscillators.
Manevitch, L.I., Kovaleva, A.S., Manevitch, E.L. (2010)
Mathematical Problems in Engineering
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Limiting phase trajectories and resonance energy transfer in a system of two coupled oscillators.
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We consider autonomous Lagrangian systems possessing two homoclinic orbits to an hyperbolic equilibrium of saddle-saddle type with two different characteristic exponents. Under a nondegeneracy assumption on the homoclinics and under suitable conditions on the geometric behaviour of these homoclinics near the equilibrium we show, by variational methods, that they give rise to an infinite family of multibump homoclinic solutions. We relax the nondegeneracy assumption when the two characteristic...