Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 126, pp. 1-26.

Title: Existence of KAM tori for presymplectic vector fields
       
Authors: Sean Bauer (Univ. of Oklahoma, Norman, OK, USA)
         Nikola P. Petrov (Univ. of Oklahoma, Norman, OK, USA)

Abstract:
  We 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.

Submitted April 5, 2019. Published December 22, 2020.
Math Subject Classifications: 34D35, 37J40, 70K43, 70H08.
Key Words: KAM theory; invariant torus; presymplectic manifold; stability.