论文标题
差异加洛依斯的方法，用于一般分析动力学系统的雅各比整合性及其应用
Differential Galoisian approach to Jacobi integrability of general analytic dynamical systems and its application
论文作者
论文摘要
Morales-Ramis理论通过差异化的Galoisian障碍物为复杂的分析性汉密尔顿系统提供了有效而强大的非整合性标准。在本文中，我们给出了有关一般分析动力学系统的Meromorormormormorphic Jacobi非整合性的新的Morales-ramis型定理。关键点是表明非线性系统的雅各布乘数的存在意味着与身份分量相关的lie代数的常见雅各布乘数存在。此外，我们将结果应用于Karabut系统的多项式整合性，以在有限深度中进行固定重力波。
The Morales-Ramis theory provides an effective and powerful non-integrability criterion for complex analytical Hamiltonian systems via the differential Galoisian obstruction. In this paper we give a new Morales-Ramis type theorem on the meromorphic Jacobi non-integrability of general analytic dynamical systems. The key point is to show the existence of Jacobian multiplier of a nonlinear system implies the existence of common Jacobian multiplier of Lie algebra associated with the identity component. In addition, we apply our results to the polynomial integrability of Karabut systems for stationary gravity waves in finite depth.
