Resonances and O-curves in Hamiltonian systems

TL;DR

This paper explores the existence of special trajectories in Hamiltonian systems that approach elliptic equilibria, especially considering the effects of resonances on these trajectories.

Contribution

It provides new insights into the behavior of Hamiltonian systems near resonant elliptic equilibria, focusing on asymptotic trajectories.

Findings

Identification of conditions for trajectories asymptotic to elliptic equilibria

Analysis of the impact of resonances on system dynamics

Development of methods to prove existence of such trajectories

Abstract

We investigate the problem of the existence of trajectories asymptotic to elliptic equilibria of Hamiltonian systems in the presence of resonances.