# On the generalization of classical Zernike system

@inproceedings{Gonera2022OnTG, title={On the generalization of classical Zernike system}, author={Cezary Gonera and Joanna Gonera and Piotr Kosiński}, year={2022} }

We generalize the results obtained recently (Nonlinearity 36 (2023), 1143) by providing a very simple proof of the superintegrability of the Hamiltonian H = ~p 2 + F ( ~q · ~p ), ~q, ~p ∈ R 2 , 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 ~q, ~p ∈ R n is sketched.

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