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A-posteriori KAM theory with optimal estimates for partially integrable systems
Univ Barcelona, Dept Matemat & Informat, Gran Via 585, E-08007 Barcelona, Spain.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
2019 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 266, no 2-3, p. 1605-1674Article in journal (Refereed) Published
Abstract [en]

In this paper we present a-posteriori KAM results for existence of d-dimensional isotropic invariant tori for n-DOF Hamiltonian systems with additional n - d independent first integrals in involution. We carry out a covariant formulation that does not require the use of action-angle variables nor symplectic reduction techniques. The main advantage is that we overcome the curse of dimensionality avoiding the practical shortcomings produced by the use of reduced coordinates, which may cause difficulties and underperformance when quantifying the hypotheses of the KAM theorem in such reduced coordinates. The results include ordinary and (generalized) iso-energetic KAM theorems. The approach is suitable to perform numerical computations and computer assisted proofs.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2019. Vol. 266, no 2-3, p. 1605-1674
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-371106DOI: 10.1016/j.jde.2018.08.003ISI: 000450909900025OAI: oai:DiVA.org:uu-371106DiVA, id: diva2:1272762
Funder
EU, European Research Council, 335079EU, Horizon 2020, MSCA 734557Available from: 2018-12-19 Created: 2018-12-19 Last updated: 2018-12-19Bibliographically approved

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Luque, Alejandro

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