标题： 代数曲线作为可分离多哈密顿系统的一个来源 显示英文标题

标题： Algebraic curves as a source of separable multi-Hamiltonian systems

摘要： 在本文中，我们系统地考虑了从平面上的代数曲线生成可积和可分离哈密顿系统的各种方法，在规范和非规范表示中。 特别是，我们考虑由平面上的2n参数代数曲线生成的两个Stäckel系统的Stäckel变换，以及由(n+N)参数代数曲线生成的Stäckel系统之间的Miura映射，导致这些系统的多哈密顿表示。 显示英文摘要

摘要： In this paper we systematically consider various ways of generating integrable and separable Hamiltonian systems in canonical and in non-canonical representations from algebraic curves on the plane. In particular, we consider St\"ackel transform between two pairs of St\"ackel systems, generated by 2n-parameter algebraic curves on the plane, as well as Miura maps between St\"ackel systems generated by (n+N)-parameter algebraic curves, leading to multi-Hamiltonian representation of these systems.