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dc.contributor.authorBauer, Sean ( )
dc.contributor.authorPetrov, Nikola ( )
dc.date.accessioned2021-10-11T21:14:17Z
dc.date.available2021-10-11T21:14:17Z
dc.date.issued2020-12-22
dc.identifier.citationBauer, S., & Petrov, N. P. (2020). Existence of KAM tori for presymplectic vector fields. Electronic Journal of Differential Equations, 2020(126), pp. 1-26.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/14636
dc.description.abstractWe prove the existence of a torus that is invariant with respect to the flow of a vector field that preserves the presymplectic form in an exact presymplectic manifold. The flow on this invariant torus is conjugate to a linear flow on a torus with a Diophantine velocity vector. The proof has an "a posteriori" format, the the invariant torus is constructed by using a Newton method in a space of functions, starting from a torus that is approximately invariant. The geometry of the problem plays a major role in the construction by allowing us to construct a special adapted basis in which the equations that need to be solved in each step of the iteration have a simple structure. In contrast to the classical methods of proof, this method does not assume that the system is close to integrable, and does not rely on using action-angle variables.en_US
dc.formatText
dc.format.extent26 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectKAM theoryen_US
dc.subjectInvariant torusen_US
dc.subjectPresymplectic manifolden_US
dc.subjectStabilityen_US
dc.titleExistence of KAM tori for presymplectic vector fieldsen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
dc.description.departmentMathematics


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