Kaiyin Huang

Jilin University


Huang K., Shi S., Li W.
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.
Keywords: Kovalevskaya exponents, weak Painlevé property, integrability, differential Galois theory, quasi-homogenous system
Citation: Huang K., Shi S., Li W.,  Kovalevskaya Exponents, Weak Painlevé Property and Integrability for Quasi-homogeneous Differential Systems, Regular and Chaotic Dynamics, 2020, vol. 25, no. 3, pp. 295-312

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