当前位置: X-MOL 学术Regul. Chaot. Dyn. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Kovalevskaya Exponents, Weak Painlevé Property and Integrability for Quasi-homogeneous Differential Systems
Regular and Chaotic Dynamics ( IF 0.8 ) Pub Date : 2020-05-31 , DOI: 10.1134/s1560354720030053
Kaiyin Huang , Shaoyun Shi , Wenlei Li

We present some necessary conditions for quasi-homogeneous differential systems to be completely integrable via Kovalevskaya exponents. Then, as an application, we give a new link between the weak-Painlevé property and the algebraical integrability for polynomial differential systems. Additionally, we also formulate stronger theorems in terms of Kovalevskaya exponents for homogeneous Newton systems, a special class of quasi-homogeneous systems, which gives its necessary conditions for B-integrability and complete integrability. A consequence is that the nonrational Kovalevskaya exponents imply the nonexistence of Darboux first integrals for two-dimensional natural homogeneous polynomial Hamiltonian systems, which relates the singularity structure to the Darboux theory of integrability.

中文翻译:

拟齐次微分系统的Kovalevskaya指数,弱Painlevé性质和可积性

我们为准齐次微分系统通过Kovalevskaya指数完全可积分提供了一些必要条件。然后,作为一个应用,我们在多项式微分系统的弱Painlevé性质和代数可积性之间建立了新的联系。此外,我们还针对齐次牛顿系统的Kovalevskaya指数(一类特殊的准齐次系统)制定了更强的定理,为B可积性和完全可积性提供了必要条件。结果是非理性的Kovalevskaya指数暗示了二维自然齐次多项式哈密顿系统不存在Darboux第一积分,这将奇异结构与Darboux可积性理论联系起来。
更新日期:2020-05-31
down
wechat
bug