Surviving Lower Dimensional Invariant Tori of a Resonant Torus with any Number of Resonances

TL;DR

This paper establishes conditions under which lower dimensional invariant tori persist in resonant Hamiltonian systems despite small perturbations, extending the understanding of stability in complex dynamical systems.

Contribution

It provides new sufficient conditions for the persistence of lower dimensional invariant tori in resonant Hamiltonian systems under small perturbations.

Findings

Sufficient conditions for invariant tori existence are identified.

Persistence of lower dimensional tori is guaranteed in resonant cases.

Results apply to arbitrary numbers of resonances.

Abstract

We provide sufficient conditions on integrable analytic Hamiltonians that guarantee the existence, under arbitrary sufficiently small analytic perturbations, of invariant lower dimensional tori associated to an invariant resonant torus of the unperturbed Hamiltonian.