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arXiv · 1703.08929

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

Misael Avendaño-Camacho·José A. Vallejo·Yury 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 works, by using singular symplectic reduction.

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Misael Avendaño-Camacho, José A. Vallejo, Yury Vorobiev. 2017-03-27. A perturbation theory approach to the stability of the Pais-Uhlenbeck oscillator. https://doi.org/10.1063/1.5000382

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