A KAM theorem for finitely differentiable Hamiltonian systems Koudjinan, Edmond ; https://orcid.org/0000-0003-2640-4049 Analysis 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. Elsevier 2020 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/8691 Koudjinan E. A KAM theorem for finitely differentiable Hamiltonian systems. <i>Journal of Differential Equations</i>. 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jde.2020.03.044 info:eu-repo/semantics/altIdentifier/issn/0022-0396 info:eu-repo/semantics/altIdentifier/arxiv/1909.04099 info:eu-repo/semantics/openAccess