Title: Generalization of solutions of the Jacobi PDEs associated to time reparametrizations of Poisson systems Show Chinese title

Title: 雅可比偏微分方程解的时间重参数化泊松系统的推广

Abstract: The determination of solutions of the Jacobi partial differential equations (PDEs) for finite-dimensional Poisson systems is considered. In particular, a novel procedure for the construction of solution families is developed. Such a procedure is based on the use of time reparametrizations preserving the existence of a Poisson structure. As a result, a method which is valid for arbitrary values of the dimension and the rank of the Poisson structure under consideration is obtained. In this article two main families of time reprametrizations of this kind are characterized. In addition, these results lead to a novel application which is also developed, namely the global and constructive determination of the Darboux canonical form for Poisson systems of arbitrary dimension and rank two, thus improving the local result provided by Darboux theorem for such a case. Show Chinese abstract

Abstract: 雅可比偏微分方程(PDEs)的解的确定对于有限维泊松系统进行了考虑。特别地，开发了一种构造解族的新程序。该程序基于使用保持泊松结构存在的时间重新参数化。因此，得到了一种适用于所考虑的泊松结构的任意维度和秩的方法。在本文中，表征了这种时间重新参数化的两个主要族。此外，这些结果导致了一个新的应用，也进行了开发，即对于任意维度和秩为二的泊松系统的达布规范形式的全局和构造性确定，从而改进了达布定理对此类情况提供的局部结果。