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Stationary Phase Methods and the Splitting of Separatrices
CSIC, Inst Ciencias Matemat, Madrid 28049, Spain.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
CSIC, Inst Ciencias Matemat, Madrid 28049, Spain.
2019 (engelsk)Inngår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 368, nr 3, s. 1297-1322Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
SPRINGER , 2019. Vol. 368, nr 3, s. 1297-1322
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Identifikatorer
URN: urn:nbn:se:uu:diva-385966DOI: 10.1007/s00220-019-03364-0ISI: 000468174000009OAI: oai:DiVA.org:uu-385966DiVA, id: diva2:1327414
Forskningsfinansiär
EU, European Research Council, 633152; 335079Knut and Alice Wallenberg Foundation, KAW 2015.0365Tilgjengelig fra: 2019-06-19 Laget: 2019-06-19 Sist oppdatert: 2019-06-19bibliografisk kontrollert

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