Cubic homogeneous polynomial centers
Li, Chengzhi (Peking University. School of Mathematical Sciences and LMAM)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2014
Abstract:	First, doing a combination of analytical and algebraic computations, we determine by first time an explicit normal form depending only on three parameters for all cubic homogeneous polynomial differential systems having a center. After using the averaging method of first order we show that we can obtain at most 1 limit cycle bifurcating from the periodic orbits of the mentioned centers when they are perturbed inside the class of all cubic polynomial differential systems. Moreover, there are examples with 1 limit cycles.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 316338
Note:	Agraïments: The first author is partially supported by NSFC-11271027 and NSFC- 11171267.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Averaging theory ; Cubic homogeneous polynomial centers ; Limit cycles
Published in:	Publicacions matemàtiques, Vol. Extra (2014) , p. 297-308, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/287219
DOI: 10.5565/PUBLMAT_Extra14_16

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Articles > Published articles > Publicacions matemàtiques
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