On the polynomial integrability of the Hoyer systems

Jaume Llibre; Clàudia Valls

doi:https://doi.org/10.1016/j.jmaa.2012.10.011

On the polynomial integrability of the Hoyer systems

Jaume Llibre, Clàudia Valls

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

1 Citation (Scopus)

Abstract

The Hoyer polynomial differential systems depend on nine parameters. We provide the necessary conditions in order that these systems have two functionally independent polynomial first integrals. We show that these conditions are not sufficient. Additionally, we illustrate how the polynomial first integrals of these systems can be computed using the Kowalevsky exponents. © 2012 Elsevier Ltd.

Original language	English
Pages (from-to)	411-417
Journal	Journal of Mathematical Analysis and Applications
Volume	399
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2012.10.011
Publication status	Published - 1 Mar 2013

Keywords

Homogeneous differential systems
Hoyer systems
Polynomial first integrals

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abstract = "The Hoyer polynomial differential systems depend on nine parameters. We provide the necessary conditions in order that these systems have two functionally independent polynomial first integrals. We show that these conditions are not sufficient. Additionally, we illustrate how the polynomial first integrals of these systems can be computed using the Kowalevsky exponents. {\textcopyright} 2012 Elsevier Ltd.",

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AB - The Hoyer polynomial differential systems depend on nine parameters. We provide the necessary conditions in order that these systems have two functionally independent polynomial first integrals. We show that these conditions are not sufficient. Additionally, we illustrate how the polynomial first integrals of these systems can be computed using the Kowalevsky exponents. © 2012 Elsevier Ltd.

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KW - Polynomial first integrals

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