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

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.

arXiv comment2 Figures. Second version. Updated bibliography and added some comments about previous works in the field

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• Stability in the higher derivative Abelian gauge field theory
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• Third order extensions of $3d$ Chern-Simons interacting to gravity: Hamiltonian formalism and stability
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• On Computational Poisson Geometry I: Symbolic Foundations
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• Nonlinear evolution of disturbances in higher time-derivative theories
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• Extended Chern-Simons model for a vector multiplet