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arXiv · 2208.05289

On the generalization of classical Zernike system

Cezary Gonera·Joanna Gonera·Piotr Kosinski
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Abstract

We generalize the results obtained recently (Nonlinearity \underline{36} (2023), 1143) by providing a very simple proof of the superintegrability of the Hamiltonian $H=\vec{p}\,^{2}+F(\vec{q}\cdot\vec{p})$, $\vec{q}, \vec{p}\in\mathbb{R}^{2}$, 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 $\vec{q}, \vec{p}\in \mathbb{R}^{n}$ is sketched.

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Cezary Gonera, Joanna Gonera, Piotr Kosinski. 2022-08-10. On the generalization of classical Zernike system. https://arxiv.org/abs/2208.05289

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