Rocky Mountain Journal of Mathematics

Invariant curves and integrability of planar $\mathcal C^r$ differential systems

Antoni Ferragut and Jaume Llibre

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Abstract

We improve the known expressions of the $\mathcal {C}^r$ differential systems in the plane having a given $\mathcal {C}^{r+1}$ invariant curve, or a given $\mathcal {C}^{r+1}$ 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.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 5 (2018), 1537-1550.

Dates
First available in Project Euclid: 19 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1539936035

Digital Object Identifier
doi:10.1216/RMJ-2018-48-5-1537

Mathematical Reviews number (MathSciNet)
MR3866558

Zentralblatt MATH identifier
06958791

Subjects
Primary: 34A05: Explicit solutions and reductions 34A34: Nonlinear equations and systems, general 34A55: Inverse problems 34C05: Location of integral curves, singular points, limit cycles 37C10: Vector fields, flows, ordinary differential equations

Keywords
Planar differential system $\mathcal C^r$ function invariant curve exponential factor cofactor Darboux theory of integrability

Citation

Ferragut, Antoni; Llibre, Jaume. Invariant curves and integrability of planar $\mathcal C^r$ differential systems. Rocky Mountain J. Math. 48 (2018), no. 5, 1537--1550. doi:10.1216/RMJ-2018-48-5-1537. https://projecteuclid.org/euclid.rmjm/1539936035


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