A KAM theorem for finitely differentiable Hamiltonian systems

article A KAM theorem for finitely differentiable Hamiltonian systems published yes Edmond Koudjinan author 52DF3E68-AEFA-11EA-95A4-124A3DDC885E0000-0003-2640-4049 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. Elsevier2020 eng Analysis Journal of Differential Equations 0022-0396 1909.0409910.1016/j.jde.2020.03.044 26964720-4750 yes Koudjinan, E. (2020). A KAM theorem for finitely differentiable Hamiltonian systems. Journal of Differential Equations. Elsevier. <a href="https://doi.org/10.1016/j.jde.2020.03.044">https://doi.org/10.1016/j.jde.2020.03.044</a> Koudjinan, Edmond. “A KAM Theorem for Finitely Differentiable Hamiltonian Systems.” Journal of Differential Equations, vol. 269, no. 6, Elsevier, 2020, pp. 4720–50, doi:<a href="https://doi.org/10.1016/j.jde.2020.03.044">10.1016/j.jde.2020.03.044</a>. Koudjinan E. 2020. A KAM theorem for finitely differentiable Hamiltonian systems. Journal of Differential Equations. 269(6), 4720–4750. E. Koudjinan, Journal of Differential Equations 269 (2020) 4720–4750. E. Koudjinan, “A KAM theorem for finitely differentiable Hamiltonian systems,” Journal of Differential Equations, vol. 269, no. 6. Elsevier, pp. 4720–4750, 2020. Koudjinan, Edmond. “A KAM Theorem for Finitely Differentiable Hamiltonian Systems.” Journal of Differential Equations. Elsevier, 2020. <a href="https://doi.org/10.1016/j.jde.2020.03.044">https://doi.org/10.1016/j.jde.2020.03.044</a>. Koudjinan E. A KAM theorem for finitely differentiable Hamiltonian systems. Journal of Differential Equations. 2020;269(6):4720-4750. doi:<a href="https://doi.org/10.1016/j.jde.2020.03.044">10.1016/j.jde.2020.03.044</a> 86912020-10-21T15:03:05Z2021-01-12T08:20:33Z