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Darboux polynomials, balances and Painlevé property

Darboux polynomials, balances and Painlevé property For a given polynomial differential system we provide different necessary conditions for the existence of Darboux polynomials using the balances of the system and the Painlevé property. As far as we know, these are the first results which relate the Darboux theory of integrability, first, to the Painlevé property and, second, to the Kovalevskaya exponents. The relation of these last two notions to the general integrability has been intensively studied over these last years. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

Darboux polynomials, balances and Painlevé property

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References (12)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Pleiades Publishing, Ltd.
Subject
Mathematics; Dynamical Systems and Ergodic Theory
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/S1560354717050057
Publisher site
See Article on Publisher Site

Abstract

For a given polynomial differential system we provide different necessary conditions for the existence of Darboux polynomials using the balances of the system and the Painlevé property. As far as we know, these are the first results which relate the Darboux theory of integrability, first, to the Painlevé property and, second, to the Kovalevskaya exponents. The relation of these last two notions to the general integrability has been intensively studied over these last years.

Journal

Regular and Chaotic DynamicsSpringer Journals

Published: Oct 1, 2017

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