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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2020, том 25, выпуск 3, страницы 295–312 (Mi rcd1065)

Эта публикация цитируется 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.

MSC: 34A34, 34C14, 34M15, 34M45

Поступила в редакцию: 19.11.2019
Принята в печать: 20.04.2020

Язык публикации: английский

DOI: 10.1134/S1560354720030053



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