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 typ...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.展开更多
In this paper,we mainly investigate three topics on the renormalization group(RG)method to singularly perturbed problems:1)We will present an explicit strategy of RG procedure to get the approximate solution up to any...In this paper,we mainly investigate three topics on the renormalization group(RG)method to singularly perturbed problems:1)We will present an explicit strategy of RG procedure to get the approximate solution up to any order.2)We will refer that the RG procedure can,in fact,be used to get the normal form of differential dynamical systems.3)We will also present the approximating center manifolds of the perturbed systems,and investigate the long time asymptotic behavior by means of RG formula.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11771177),National Natural Science Foundation of China(Grant Nos.12001386 and 12090013)Science and Technology Development Project of Jilin Province(Grant No.YDZJ202101ZYTS141)+1 种基金supported by Sichuan University Postdoctoral Interdisciplinary Innovation Fund(Grant No.0020104153010)the Fundamental Research Funds for the Central Universities(Grant No.20826041E4168)。
文摘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.
基金NSFC grant(Nos.11771177,12171197)China Auto-mobile Industry Innovation and Development Joint Fund(No.U1664257)Program for Changbaishan Scholars of Jilin Province and Science and Technology Development Project of Jilin Province(No.YDZJ202101ZYTS141,20190201132JC).
文摘In this paper,we mainly investigate three topics on the renormalization group(RG)method to singularly perturbed problems:1)We will present an explicit strategy of RG procedure to get the approximate solution up to any order.2)We will refer that the RG procedure can,in fact,be used to get the normal form of differential dynamical systems.3)We will also present the approximating center manifolds of the perturbed systems,and investigate the long time asymptotic behavior by means of RG formula.
