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

M. Avendaño-Camacho; J. A. Vallejo; Yu Vorobiev

doi:10.1063/1.5000382

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

M. Avendaño-Camacho, J. A. Vallejo, Yu Vorobiev

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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 studies, by using singular symplectic reduction.

Original language	English
Article number	093501
Journal	Journal of Mathematical Physics
Volume	58
Issue number	9
DOIs	https://doi.org/10.1063/1.5000382
State	Published - 1 Sep 2017

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AB - 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 studies, by using singular symplectic reduction.

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

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