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2019-01-15

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cc-by-nc-nd (c) Elsevier, 2019
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/192651

A-posteriori KAM theory with optimal estimates for partially integrable systems

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https://doi.org/10.1016/j.jde.2018.08.003

Abstract

ABSTRACT. 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.

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Sistemes dinàmics de baixa dimensió, Teoria ergòdica, Dinàmica topològica, Sistemes dinàmics aleatoris

Subject (English)

Low-dimensional dynamical systems, Ergodic theory, Topological dynamics, Random dynamical systems

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HARO, Àlex and LUQUE, Alejandro. A-posteriori KAM theory with optimal estimates for partially integrable systems. Journal of Differential Equations. 2019. Vol. 266, num. 2-3, pags. 1605-1674. ISSN 0022-0396. [consulted: 19 of August of 2026]. Available at: https://hdl.handle.net/2445/192651

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