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

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...

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Bibliographic Details
Published in:arXiv.org 2017-05
Main Authors: Avendaño-Camacho, Misael, Vallejo, José A, Vorobiev, Yury
Format: Article
Language:English
Subjects:
Hamiltonian functions
Orbital stability
Perturbation theory
Stability analysis
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1703.08929