Instability-driven energy transport in near-integrable, many degrees-of-freedom, Hamiltonian systems

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Abstract
We report a numerical study of near-integrable Hamiltonian systems with many degrees of freedom. Recently reported transition phenomena for a coarse discrete sine-Gordon system are reexamined in the near-integrable limit and with the aid of statistical and integrable diagnostics. We show that the critical energy of transition from recurrence to chaotic transport of energy coincides with the onset, in the initial data, of integrable exponential instabilities and associated homoclinic orbits. This Letter aims to tie together classical and recent numerical experiments and theory of lattice instabilities and integrable systems.