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.

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

References in corpus (11)

• Classical and quantum stability of higher-derivative dynamics
• Stable Self-Interacting Pais-Uhlenbeck Oscillator
• Comments on the Dynamics of the Pais-Uhlenbeck Oscillator
• Pais-Uhlenbeck Oscillator and Negative Energies
• Some Comments on Ghosts and Unitarity: The Pais-Uhlenbeck Oscillator Revisited
• Pais-Uhlenbeck Oscillator with a Benign Friction Force
• An alternative Hamiltonian formulation for the Pais-Uhlenbeck oscillator
• r${}_{\infty }$-Matrices, triangular L${}_{\infty }$-bialgebras, and quantum${}_{\infty }$ groups
• Quantum Field Theories in Spaces with Neutral Signatures
• A simple global representation for second-order normal forms of Hamiltonian systems relative to periodic flows
• Energy and stability of Pais-Uhlenbeck oscillator

Cited by in corpus (17)

• Is negative kinetic energy meta-stable?
• Stable interactions in higher derivative field theories of derived type
• Multi-Hamiltonian formulations and stability of higher-derivative extensions of $3d$ Chern-Simons
• Higher-derivative harmonic oscillators: stability of classical dynamics and adiabatic invariants
• Resonance and stability of higher derivative theories of derived type
• Conservation Laws and Stability of Field Theories of Derived Type
• Confining complex ghost degrees of freedom
• Higher time-derivative theories from space-time interchanged integrable field theories
• Stability in the higher derivative Abelian gauge field theory
• Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
• Third order extensions of $3d$ Chern-Simons interacting to gravity: Hamiltonian formalism and stability
• Integrable scattering theory with higher derivative Hamiltonians
• On Computational Poisson Geometry I: Symbolic Foundations
• On Computational Poisson Geometry II: Numerical Methods
• Nonlinear evolution of disturbances in higher time-derivative theories
• Hamiltonian systems: symbolical, numerical and graphical study
• Extended Chern-Simons model for a vector multiplet