论文标题
非天然哈密顿人的扩展
Extensions of non-natural Hamiltonians
论文作者
论文摘要
扩展的哈密顿系统的概念允许对几个可集成和整合系统的几何解释，该系统具有多项式第一积分，具体取决于有理参数。到目前为止，仅在天然哈密顿人的情况下才采用扩展程序。在本文中，我们为非天然的哈密顿人提供了几个示例，例如两个点涡流，Lotka-Volterra和一些在Momenta Hamiltonians中的四分之一Quartic，在某些情况下可以有效地扩展汉密尔顿人，而在其他情况下则失败了。我们简要讨论这些结果的原因。
The concept of extended Hamiltonian systems allows the geometrical interpretation of several integrable and superintegrable systems with polynomial first integrals of degree depending on a rational parameter. Until now, the procedure of extension has been applied only in the case of natural Hamiltonians. In this article, we give several examples of application to non-natural Hamiltonians, such as the two point-vortices, the Lotka-Volterra and some quartic in the momenta Hamiltonians, obtaining effectively extended Hamiltonians in some cases and failing in others. We briefly discuss the reasons of these results.
