Differential Galoisian approach to Jacobi integrability of general analytic dynamical systems and its application
Differential Galoisian approach to Jacobi integrability of general analytic dynamical systems and its application
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DOI：
10.1007/s11425-021-2015-6
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发表时间：
2022-08
期刊：
影响因子：
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通讯作者：
Kaiyin Huang;S. Shi;Shuangling Yang
中科院分区：
文献类型：
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作者：
Kaiyin Huang;S. Shi;Shuangling Yang
Morales-Ramis理论通过微分Galoisian阻挡为复解析哈密顿系统提供了一个有效且强大的不可积判据。本文给出了一般解析动力系统亚纯Jacobi不可积的一个新的Morales-Ramis型定理。证明了非线性系统的雅可比乘子的存在意味着与单位分量相关的李代数的公共雅可比乘子的存在。此外，我们还将我们的结果应用于有限深度定常重力波的Karabut系统的多项式可积性。
The Morales-Ramis theory provides an effective and powerful non-integrability criterion for complex analytic 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 that the existence of Jacobian multipliers of a nonlinear system implies the existence of common Jacobian multipliers 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.