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arXiv · 1803.07845

Stationary phase methods and the splitting of separatrices

Alberto Enciso·Alejandro Luque·Daniel Peralta-Salas
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Abstract

Using stationary phase methods, we provide an explicit formula for the Melnikov function of the one and a half degrees of freedom system given by a Hamiltonian system subject to a rapidly oscillating perturbation. Remarkably, the Melnikov function turns out to be computable without an explicit knowledge of the separatrix and in the case of non-analytic systems. This is related to a priori stable systems coupled with low regularity perturbations. It also applies to perturbations controlled by wave-type equations, so in particular we also illustrate this result with the motion of charged particles in a rapidly oscillating electromagnetic field. Quasiperiodic perturbations are discussed too.

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Alberto Enciso, Alejandro Luque, Daniel Peralta-Salas. 2018-03-21. Stationary phase methods and the splitting of separatrices. https://doi.org/10.1007/s00220-019-03364-0

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