Bauer, SeanPetrov, Nikola2021-10-112021-10-112020-12-22Bauer, S., & Petrov, N. P. (2020). Existence of KAM tori for presymplectic vector fields. <i>Electronic Journal of Differential Equations, 2020</i>(126), pp. 1-26.1072-6691https://hdl.handle.net/10877/14636We prove the existence of a torus that is invariant with respect to the flow of a vector field that preserves the presymplectic form in an exact presymplectic manifold. The flow on this invariant torus is conjugate to a linear flow on a torus with a Diophantine velocity vector. The proof has an "a posteriori" format, the the invariant torus is constructed by using a Newton method in a space of functions, starting from a torus that is approximately invariant. The geometry of the problem plays a major role in the construction by allowing us to construct a special adapted basis in which the equations that need to be solved in each step of the iteration have a simple structure. In contrast to the classical methods of proof, this method does not assume that the system is close to integrable, and does not rely on using action-angle variables.Text26 pages1 file (.pdf)enAttribution 4.0 InternationalKAM theoryInvariant torusPresymplectic manifoldStabilityArticle