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Эта публикация цитируется в 7 научных статьях (всего в 7 статьях)
Kovalevskaya Exponents, Weak Painlevé Property and Integrability for Quasi-homogeneous Differential Systems
Kaiyin Huanga, Shaoyun Shibc, Wenlei Li a School of Mathematics, Sichun University,
Chengdu 610000, China
b State Key Laboratory of Automotive Simulation and Control,
Jilin University, Changchun 130012, P.R. China
c School of Mathematics, Jilin University,
Changchun 130012, China
Аннотация:
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.
Ключевые слова:
Kovalevskaya exponents, weak Painlevé property, integrability, differential Galois
theory, quasi-homogenous system.
Поступила в редакцию: 19.11.2019 Принята в печать: 20.04.2020
Образец цитирования:
Kaiyin Huang, Shaoyun Shi, Wenlei Li, “Kovalevskaya Exponents, Weak Painlevé Property and Integrability for Quasi-homogeneous Differential Systems”, Regul. Chaotic Dyn., 25:3 (2020), 295–312
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd1065 https://www.mathnet.ru/rus/rcd/v25/i3/p295
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