Periodic orbits in the case of a zero eigenvalue

TL;DR

This paper demonstrates that in dynamical systems with sufficient constants of motion, a Moser-Weinstein type theorem can establish the existence of periodic orbits even when the linearized system is degenerate.

Contribution

It extends the application of Moser-Weinstein theorem to cases with zero eigenvalues, providing a new method for proving periodic orbits in degenerate systems.

Findings

Existence of periodic orbits in degenerate systems proven

Application of Moser-Weinstein theorem to systems with zero eigenvalues

Conditions for constants of motion to guarantee periodic orbits

Abstract

We will show that if a dynamical system has enough constants of motion then a Moser-Weinstein type theorem can be applied for proving the existence of periodic orbits in the case when the linearized system is degenerate.