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

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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 languageEnglish
Article number093501
JournalJournal of Mathematical Physics
Volume58
Issue number9
DOIs
StatePublished - 1 Sep 2017

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