Branching of periodic orbits in reversible hamiltonian systems

TL;DR

This paper investigates the existence of reversible periodic orbits near elliptic equilibria in time-reversible Hamiltonian systems with 2 and 3 degrees of freedom, using normal form and reduction techniques.

Contribution

It provides new results on families of reversible periodic solutions in Hamiltonian systems with symmetries, employing Birkhoff and Belitskii normal forms.

Findings

Existence of one-parameter families of reversible periodic solutions

Periodic solutions terminate at the elliptic equilibrium

Application of normal form and Liapunov-Schmidt reduction techniques

Abstract

This paper deals with the dynamics of time-reversible Hamiltonian vector fields with 2 and 3 degrees of freedom around an elliptic equilibrium point in presence of symplectic involutions. The main results discuss the existence of one-parameter families of reversible periodic solutions terminating at the equilibrium. The main techniques used are Birkhoff and Belitskii normal forms combined with the Liapunov-Schmidt reduction.