Conformal Newton–Hooke symmetry of Pais–Uhlenbeck oscillator

It is demonstrated that the Pais–Uhlenbeck oscillator in arbitrary dimension enjoys the l  -conformal Newton–Hooke symmetry provided frequencies of oscillation form the arithmetic sequence ωk=(2k−1)ω1ωk=(2k−1)ω1, where k=1,…,nk=1,…,n, and l   is the half-integer 2n−12. The model is shown to be maximally superintegrable. A link to n decoupled isotropic oscillators is discussed and an interplay between the l-conformal Newton–Hooke symmetry and symmetries characterizing each individual isotropic oscillator is analyzed.