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• W4313592222 endingPage "1167" @default.
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• W4313592222 abstract "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 $q_i$ and $p_i$ are generic canonical variables, $gamma_n$ are arbitrary coefficients, and $Nin mathbb N$. For $N=2$, being both $gamma_1,gamma_2$ different from zero, this reduces to the classical Zernike system. We prove that $mathcal H_N$ always provides a superintegrable system (for any value of $gamma_n$ and $N$) by obtaining the corresponding constants of the motion explicitly, which turn out to be of higher-order in the momenta. Such generic results are not only applied to the Euclidean plane, but also to the sphere and the hyperbolic plane. In the latter curved spaces, $mathcal H_N $ is expressed in geodesic polar coordinates showing that such a new superintegrable Hamiltonian can be regarded as a superposition of the isotropic 1:1 curved (Higgs) oscillator with even-order anharmonic curved oscillators plus another superposition of higher-order momentum-dependent potentials. Furthermore, the symmetry algebra determined by the constants of the motion is also studied, giving rise to a $(2N-1)$th-order polynomial algebra. As a byproduct, the Hamiltonian $mathcal H_N $ is interpreted as a family of superintegrable perturbations of the classical Zernike system. Finally, it is shown that $mathcal H_N$ (and so the Zernike system as well) is endowed with a Poisson $mathfrak{sl}(2,mathbb R)$-coalgebra symmetry which would allow for further possible generalizations that are also discussed." @default.
• W4313592222 created "2023-01-06" @default.
• W4313592222 creator A5004684986 @default.
• W4313592222 creator A5014666885 @default.
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• W4313592222 date "2023-01-04" @default.
• W4313592222 modified "2023-09-30" @default.
• W4313592222 title "Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system" @default.
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• W4313592222 doi "https://doi.org/10.1088/1361-6544/acad5e" @default.
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