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Centers of weight-homogeneous polynomial vector fields on the plane


Authors: Jaume Giné, Jaume Llibre and Claudia Valls
Journal: Proc. Amer. Math. Soc. 145 (2017), 2539-2555
MSC (2010): Primary 37D99
DOI: https://doi.org/10.1090/proc/13393
Published electronically: December 9, 2016
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Abstract: We characterize all centers of planar weight-homogeneous polynomial vector fields. Moreover we classify all centers of planar weight-
homogeneous polynomial vector fields of degrees $ 6$ and $ 7$.


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Additional Information

Jaume Giné
Affiliation: Departament de Matemàtica, Universitat de Lleida, Avda. Jaume II, 69, 25001 Lleida, Catalonia, Spain
Email: gine@matematica.udl.cat

Jaume Llibre
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bella- terra, Barcelona, Catalonia, Spain
Email: jllibre@mat.uab.cat

Claudia Valls
Affiliation: Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
Email: cvalls@math.ist.utl.pt

DOI: https://doi.org/10.1090/proc/13393
Keywords: Hopf bifurcation, chaotic system, Darboux integrability, Poincar\'e compactification, weight-homogeneous polynomial differential systems, quasi-homogeneous polynomial differential systems.
Received by editor(s): July 31, 2015
Received by editor(s) in revised form: May 12, 2016, and July 22, 2016
Published electronically: December 9, 2016
Additional Notes: The first author was partially supported by MINECO/FEDER grant number MTM2014-53703-P and AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204
The second author was partially supported by MINECO grant MTM2013-40998-P, AGAUR grant number 2014 SGR568, the grants FP7-PEOPLE-2012-IRSES 318999 and 316338, and the MINECO/FEDER grant UNAB13-4E-1604
The third author was partially supported by FCT/Portugal through UID/MAT/04459/2013
Communicated by: Yingfei Yi
Article copyright: © Copyright 2016 American Mathematical Society