Conformal symmetry in damped Pais-Uhlenbeck oscillator

Abstract: Two Lagrangian formulations for describing of the damped harmonic oscillator have been introduced by Bateman. For these models we construct higher derivative generalization which enjoys the l-conformal Newton-Hooke symmetry. The dynamics of generalized systems corresponds to the damped Pais-Uhlenbeck oscillator for a particular choice of its frequencies.