On the planar integrable differential systems

Jaume Giné; Jaume Llibre

doi:https://doi.org/10.1007/s00033-011-0116-5

On the planar integrable differential systems

Jaume Giné, Jaume Llibre

Department of Mathematics

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

10 Citations (Scopus)

Abstract

In this paper, we prove that the C1 planar differential systems that are integrable and non-Hamiltonian roughly speaking are C1 equivalent to the linear differential systems. Additionally, we show that these systems have always a Lie symmetry. These results are improved for the class of polynomial differential systems defined in R2 or C2. © 2011 Springer Basel AG.

Original language	English
Pages (from-to)	567-574
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	62
Issue number	4
DOIs	https://doi.org/10.1007/s00033-011-0116-5
Publication status	Published - 1 Aug 2011

Keywords

Darboux theory of integrability
Linear differential systems
Planar integrability
Polynomial differential systems

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https://ddd.uab.cat/record/150422

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abstract = "In this paper, we prove that the C1 planar differential systems that are integrable and non-Hamiltonian roughly speaking are C1 equivalent to the linear differential systems. Additionally, we show that these systems have always a Lie symmetry. These results are improved for the class of polynomial differential systems defined in R2 or C2. {\textcopyright} 2011 Springer Basel AG.",

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AU - Llibre, Jaume

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AB - In this paper, we prove that the C1 planar differential systems that are integrable and non-Hamiltonian roughly speaking are C1 equivalent to the linear differential systems. Additionally, we show that these systems have always a Lie symmetry. These results are improved for the class of polynomial differential systems defined in R2 or C2. © 2011 Springer Basel AG.

KW - Darboux theory of integrability

KW - Linear differential systems

KW - Planar integrability

KW - Polynomial differential systems

U2 - https://doi.org/10.1007/s00033-011-0116-5

DO - https://doi.org/10.1007/s00033-011-0116-5

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JF - Zeitschrift fur Angewandte Mathematik und Physik

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ER -

On the planar integrable differential systems

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Keywords

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