A KAM theorem for generalized Hamiltonian systems without action-angle variables

TL;DR

This paper establishes a KAM theorem for generalized Hamiltonian systems lacking action-angle variables, extending previous results to a broader class of systems.

Contribution

It generalizes the KAM theorem to systems without action-angle variables, broadening the scope of invariant torus existence results.

Findings

Proved a KAM theorem for generalized Hamiltonian systems without action-angle variables.

Extended previous results from canonical Hamiltonian systems to more general systems.

Established conditions for the persistence of invariant tori in these systems.

Abstract

We proved a KAM theorem on existence of invariant tori in generalized Hamiltonian systems without action-angle variables. It is a generalization of the result of de la Llave et al. [Llave, 2005] that deals with canonical Hamiltonian system.