Polynomial integrability of natural two-dimensional Hamiltonian systems and applications

自然二维哈密顿系统的多项式可积性及应用

• 批准号: 455806247
• 负责人: Professor Dr. Vladimir Matveev
• 金额: --
• 依托单位: Lehrstuhl für Differentialgeometrie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/455806247?language=en
• 关键词: Polynomial; integrability; natural; two; dimensional

Our project deals with integrable Hamiltonian systems with two degrees of freedom. We study the existence of integrals which are polynomial in momenta. We intend to apply new developed methods in order to construct new phyiscally interesting examples of such systems and tackle a number of famous conjectures. In particular, we plan to solve two conjectures attributed to Birkhoff and the problem of Whittaker. We aim to study the natural generalisations of such systems for magnetic flows and apply obtained results in Finsler geometry and general relativity. Further, we study integrability of magnetic and Finsler billiards.

我们的项目涉及两个自由度的可积哈密顿系统。研究了动量多项式积分的存在性。我们打算应用新开发的方法，以构建新的phyiscally有趣的例子，这样的系统，并解决一些著名的acquitures。特别是，我们计划解决两个问题归因于伯克霍夫和惠特克的问题。我们的目标是研究自然概括的磁流和芬斯勒几何和广义相对论中得到的结果，这样的系统。进一步，我们研究了磁台球和Finsler台球的可积性.