Existence of Invariant Tori for Differentiable Hamiltonian Vector Fields without Action-Angle Variables

TL;DR

This paper proves the existence of invariant tori in differentiable Hamiltonian vector fields without relying on action-angle variables, extending previous results that were limited to analytic vector fields.

Contribution

It generalizes the existence of invariant tori to differentiable Hamiltonian systems, removing the need for action-angle variables and extending prior analytic results.

Findings

Invariant tori exist in differentiable Hamiltonian vector fields.

The result generalizes previous analytic cases.

Provides a broader applicability for Hamiltonian dynamics.

Abstract

We proved the existence of invariant tori in differentiable Hamiltonian vector fields without action-angle variables. It is a generalization of the result of [Llave, 2005] that deals with analytic vector fields.