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Título:	Zero-Hopf polynomial centers of third-order differential equations
Autor/a:	García, I. A. (Isaac A.); Valls, Claudia
Notas:	We study the 3-dimensional center problem at the zero-Hopf singularity in some families of polynomial vector fields arising from third-order polynomial differential equations. After proving some general properties we check that the quadratic family has no 3-dimensional centers. Later we characterize all the 3-dimensional centers in the cubic homogeneous family. Finally we give a partial classification of the 3-dimensional centers at just one singularity of the full cubic family and propose one open problem to close this classification. The first author is partially supported by a MINECO grant number MTM2014-53703-P and an AGAUR grant number 2014SGR 1204. The second author is supported by Portuguese National Funds through FCT - Fundaçao para a Ciencia e a Tecnologia within CAMGSD and the project PTDC/MAT/117106/2010.
Materia(s):	-Zero-Hopf singularity -Three-dimensional vector fields -Continua of periodic orbits -Poincaré map
Derechos:	(c) Springer Science+Business Media New York, 2016
Tipo de documento:	Artículo Artículo - Versión aceptada
Editor:	Springer Science+Business Media New York
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