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

9 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

Access to Document

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

Fingerprint Dive into the research topics of 'On the planar integrable differential systems'. Together they form a unique fingerprint.

Cite this

@article{bbbb6024e99f45869ead6ae833d33f99,

title = "On the planar integrable differential systems",

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.",

keywords = "Darboux theory of integrability, Linear differential systems, Planar integrability, Polynomial differential systems",

author = "Jaume Gin{\'e} and Jaume Llibre",

year = "2011",

month = aug,

day = "1",

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

language = "English",

volume = "62",

pages = "567--574",

journal = "Zeitschrift fur Angewandte Mathematik und Physik",

issn = "0044-2275",

publisher = "Birkhauser Verlag Basel",

number = "4",

}

TY - JOUR

T1 - On the planar integrable differential systems

AU - Giné, Jaume

AU - Llibre, Jaume

PY - 2011/8/1

Y1 - 2011/8/1

N2 - 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.

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

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

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

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

M3 - Article

VL - 62

SP - 567

EP - 574

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

SN - 0044-2275

IS - 4

ER -

On the planar integrable differential systems

Abstract

Keywords

Access to Document

Other files and links

Cite this