Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system

Alfonso Blasco, Ivan Gutierrez-Sagredo, Francisco J. Herranz

We consider the classical momentum- or velocity-dependent two-dimensional Hamiltonian given by $${\mathcal{H}}_N=p_1^2+p_2^2+\sum _{n=1}^N{\gamma }_n(q_1{p}_1+q_2{p}_2{)}^n,$$ where $q_i$…