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Stationary Phase Methods and the Splitting of Separatrices
CSIC, Inst Ciencias Matemat, Madrid 28049, Spain.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
CSIC, Inst Ciencias Matemat, Madrid 28049, Spain.
2019 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 368, no 3, p. 1297-1322Article in journal (Refereed) Published
Abstract [en]

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 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.

Place, publisher, year, edition, pages
SPRINGER , 2019. Vol. 368, no 3, p. 1297-1322
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Other Physics Topics Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-385966DOI: 10.1007/s00220-019-03364-0ISI: 000468174000009OAI: oai:DiVA.org:uu-385966DiVA, id: diva2:1327414
Funder
EU, European Research Council, 633152; 335079Knut and Alice Wallenberg Foundation, KAW 2015.0365Available from: 2019-06-19 Created: 2019-06-19 Last updated: 2019-06-19Bibliographically approved

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Luque, Alejandro

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