Hyperbolic Orbits for a Class of Singular Hamiltonian Systems with Repulsive Potentials

TL;DR

This paper proves the existence of hyperbolic orbits in certain singular Hamiltonian systems with repulsive potentials by using a limiting process on periodic solutions that minimize a variational functional.

Contribution

It introduces a novel method of establishing hyperbolic orbits through variational minimization and limit processes in singular Hamiltonian systems.

Findings

Existence of hyperbolic orbits established

Method based on limit of periodic minimizers

Applicable to systems with repulsive potentials

Abstract

The existence of hyperbolic orbits is proved for a class of singular Hamiltonian systems with repulsive potentials by taking limit for a sequence of periodic solutions which are the minimizers of variational functional