Limit cycles for a class of quintic Z_6 equivariant systems without infinite critical points
Álvarez Torres, María Jesús (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)
Laboriau, Isabel S. (Centro de Matemática da Universidade do Porto (Portugal))
Murza, Adrian (Centro de Matemática da Universidade do Porto (Portugal))

Date:	2014
Abstract:	We analyze the dynamics of a class of Z_6-equivariant systems of the form =pz^2 sz^3^2-^5, where z is complex, the time t is real, while p and s are complex parameters. This study is the natural continuation of a previous work (M. J. \'Alvarez, A. Gasull, R. Prohens, Proc. Am. Math. Soc. 136, (2008), 1035--1043) on the normal form of Z_4-equivariant systems. Our study uses the reduction of the equation to an Abel one, and provide criteria for proving in some cases uniqueness and hyperbolicity of the limit cycle surrounding either 1, 7 or 13 critical points, the origin being always one of these points.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437
Note:	Agraïments/Ajudes: M.J.A. was partially supported by grant MTM2008-03437. I.S.L. and A.C.M. were partially supported by the European Regional Development Fund through the programme COMPETE and through the Funda ̧câo para a Ciência e a Tecnologia (FCT) under the project PEst-C/MAT/UI0144/2013. A.C.M. was also supported by the grant SFRH/ BD/
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycles ; Planar autonomous ordinary differential equations ; Symmetric polinomial systems
Published in:	Bulletin of the Belgian Mathematical Society. Simon Stevin, Vol. 21 (2014) , p. 841-857, ISSN 1370-1444

Postprint 16 p, 478.3 KB

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