论文标题
关于古典Zernike系统的概括
On the generalization of classical Zernike system
论文作者
论文摘要
我们通过提供一个非常简单的证据证明哈密顿式$ h = \ vec {p} \，^{2} {2}+f（\ vec {q} {q} \ cdot \ cdot \ vec {p}，对于任何分析函数$ f $，\ vec {p} \ in \ mathbb {r}^{2} $。额外的运动积分是明确构建的，并显示为多项式$ f $的规范变量中的多项式。对情况的概括$ \ vec {q}，\ vec {p} \ in \ mathbb {r}^{n} $的概括。
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.
