A KAM theorem for finitely differentiable Hamiltonian systems

E. Koudjinan, Journal of Differential Equations 269 (2020) 4720–4750.


Journal Article | Published | English
Abstract
Given l>2ν>2d≥4, we prove the persistence of a Cantor--family of KAM tori of measure O(ε1/2−ν/l) for any non--degenerate nearly integrable Hamiltonian system of class Cl(D×Td), where D⊂Rd is a bounded domain, provided that the size ε of the perturbation is sufficiently small. This extends a result by D. Salamon in \cite{salamon2004kolmogorov} according to which we do have the persistence of a single KAM torus in the same framework. Moreover, it is well--known that, for the persistence of a single torus, the regularity assumption can not be improved.
Keywords
Publishing Year
Date Published
2020-09-05
Journal Title
Journal of Differential Equations
Volume
269
Issue
6
Page
4720-4750
ISSN
IST-REx-ID

Cite this

Koudjinan E. A KAM theorem for finitely differentiable Hamiltonian systems. Journal of Differential Equations. 2020;269(6):4720-4750. doi:10.1016/j.jde.2020.03.044
Koudjinan, E. (2020). A KAM theorem for finitely differentiable Hamiltonian systems. Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2020.03.044
Koudjinan, Edmond. “A KAM Theorem for Finitely Differentiable Hamiltonian Systems.” Journal of Differential Equations. Elsevier, 2020. https://doi.org/10.1016/j.jde.2020.03.044.
E. Koudjinan, “A KAM theorem for finitely differentiable Hamiltonian systems,” Journal of Differential Equations, vol. 269, no. 6. Elsevier, pp. 4720–4750, 2020.
Koudjinan E. 2020. A KAM theorem for finitely differentiable Hamiltonian systems. Journal of Differential Equations. 269(6), 4720–4750.
Koudjinan, Edmond. “A KAM Theorem for Finitely Differentiable Hamiltonian Systems.” Journal of Differential Equations, vol. 269, no. 6, Elsevier, 2020, pp. 4720–50, doi:10.1016/j.jde.2020.03.044.
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