Invariant curves and integrability of planar cr differential systems

Antoni Ferragut; Jaume Llibre

doi:https://doi.org/10.1216/RMJ-2018-48-5-1537

Invariant curves and integrability of planar c^r differential systems

Antoni Ferragut, Jaume Llibre

Department of Mathematics

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

Abstract

Copyright © 2018 Rocky Mountain Mathematics Consortium. We improve the known expressions of the Cr differential systems in the plane having a given Cr+1 invariant curve, or a given Cr+1 first integral. Their application to polynomial differential systems having either an invariant algebraic curve, or a first integral, also improves the known results on such systems.

Original language	English
Pages (from-to)	1537-1550
Journal	Rocky Mountain Journal of Mathematics
Volume	48
Issue number	5
DOIs	https://doi.org/10.1216/RMJ-2018-48-5-1537
Publication status	Published - 1 Jan 2018

Keywords

Cofactor
Cr function
Darboux theory of integrability
Exponential factor
Invariant curve
Planar differential system

Access to Document

https://doi.org/10.1216/RMJ-2018-48-5-1537

https://ddd.uab.cat/record/221313

Cite this

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abstract = "Copyright {\textcopyright} 2018 Rocky Mountain Mathematics Consortium. We improve the known expressions of the Cr differential systems in the plane having a given Cr+1 invariant curve, or a given Cr+1 first integral. Their application to polynomial differential systems having either an invariant algebraic curve, or a first integral, also improves the known results on such systems.",

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KW - Cofactor

KW - Cr function

KW - Darboux theory of integrability

KW - Exponential factor

KW - Invariant curve

KW - Planar differential system

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