On the generalization of classical Zernike system

Abstract

We generalize the results obtained recently (Blasco et al 2023 Nonlinearity 36 1143) by providing a very simple proof of the superintegrability of the Hamiltonian H=p⃗2+F(q⃗⋅p⃗) , q⃗,p⃗∈R2 , for any analytic function F. The additional integral of motion is constructed explicitly and shown to reduce to a polynomial in canonical variables for polynomial F. The generalization to the case q⃗,p⃗∈Rn is sketched.