# A perturbation theory approach to the stability of the Pais-Uhlenbeck oscillator

## TL;DR

This paper analyzes the stability of the Pais-Uhlenbeck oscillator using advanced Hamiltonian techniques, providing explicit phase space descriptions and proving the existence of stable orbits for specific self-interactions.

## Contribution

It introduces a novel application of Lie-Deprit series and Hamiltonian normal form theories to the Pais-Uhlenbeck oscillator, including explicit phase space reduction and stability proofs.

## Key findings

- Explicit phase space description for the oscillator
- Proof of stable orbits for certain self-interactions
- Application of singular symplectic reduction techniques

## Abstract

We present a detailed analysis of the orbital stability of the Pais-Uhlenbeck oscillator, using Lie-Deprit series and Hamiltonian normal form theories. In particular, we explicitly describe the reduced phase space for this Hamiltonian system and give a proof for the existence of stable orbits for a certain class of self-interaction, found numerically in previous works, by using singular symplectic reduction.