Rocky Mountain Journal of Mathematics

Integrability of reversible and equivariant quadratic polynomial differential systems in the plane

Jaume Llibre and Claudia Valls

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We study the existence of first integrals for the class of reversible and equivariant quadratic polynomial differential systems in the plane. We put special emphasis in the study of the analytic first integrals.


The first author was partially supported by the Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación, grant No. MTM2016-77278-P (FEDER), the Agència de Gestió d’Ajuts Universitaris i de Recerca, grant No. 2017SGR1617 and the H2020 European Research Council, grant No. MSCA-RISE-2017-777911. The second author was partially supported by FCT/Portugal through UID/MAT/04459/2013.

Article information

Rocky Mountain J. Math., Volume 49, Number 2 (2019), 579-591.

Received: 10 July 2014
Revised: 26 September 2018
First available in Project Euclid: 23 June 2019

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Zentralblatt MATH identifier

Primary: 34C07: Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) 34C08: Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.) 37J35: Completely integrable systems, topological structure of phase space, integration methods

reversible equivariant quadratic planar polynomial equations analytic first integral


Llibre, Jaume; Valls, Claudia. Integrability of reversible and equivariant quadratic polynomial differential systems in the plane. Rocky Mountain J. Math. 49 (2019), no. 2, 579--591. doi:10.1216/RMJ-2019-49-2-579.

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