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Stationary phase methods and the splitting of separatrices

AuthorsEnciso, Alberto; Luque, Alejandro ; Peralta-Salas, Daniel
Issue Date13-Feb-2019
CitationCommunications in Mathematical Physics (2019)
AbstractUsing 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 using very little information on the separatrix and in the case of non-analytic systems. This is related to a priori stable systems coupled with low regularity perturbations. A natural physical application is 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. Quasi-periodic perturbations are discussed too.
Publisher version (URL)http://dx.doi.org/10.1007/s00220-019-03364-0
Identifiersdoi: 10.1007/s00220-019-03364-0
issn: 1432-0916
Appears in Collections:(ICMAT) Artículos
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