Hyperbolic Orbits for a Class of Singular Hamiltonian Systems

TL;DR

This paper proves the existence of hyperbolic orbits in certain singular Hamiltonian systems by analyzing the limits of variationally minimized periodic solutions.

Contribution

It introduces a novel approach to establish hyperbolic orbits using limit processes of variational minimizers in singular Hamiltonian systems.

Findings

Existence of hyperbolic orbits proven for specific Hamiltonian systems

Method based on limits of periodic solutions as variational minimizers

Applicable to a class of singular Hamiltonian systems

Abstract

The existence of hyperbolic orbits is proved for a class of singular Hamiltonian systems $\ddot{u}(t)+\nabla V(u(t))=0$ by taking limit for a sequence of periodic solutions which are the variational minimizers of Lagrangian actions.