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Kovalevskaya Exponents, Weak Painlevé Property and Integrability for Quasi-homogeneous Differential Systems

Kovalevskaya Exponents, Weak Painlevé Property and Integrability for Quasi-homogeneous... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

Kovalevskaya Exponents, Weak Painlevé Property and Integrability for Quasi-homogeneous Differential Systems

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References (41)

Publisher
Springer Journals
Copyright
Copyright © Pleiades Publishing, Ltd. 2020
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/S1560354720030053
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Regular and Chaotic DynamicsSpringer Journals

Published: May 31, 2020

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