Global phase portraits of uniform isochronous centers with quartic homogeneous polynomial nonlinearities
Itikawa, Jackson (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2016
Abstract:	We classify the global phase portraits in the Poincar\'e disc of the differential systems =-y xf(x,y), =x yf(x,y), where f(x,y) is a homogeneous polynomial of degree 3. These systems have a uniform isochronous center at the origin. This paper together with the results presented in IL2 completes the classification of the global phase portraits in the Poincar\'e disc of all quartic polynomial differential systems with a uniform isochronous center at the origin.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad MTM2013-40998-P Ministerio de Economía y Competitividad UNAB13-4E-1604 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 318999 European Commission 316338
Note:	Agraïments: The first author is is supported by a Ciência sem Fronteiras-CNPq grant number 201002/ 2012-4. A CAPES grant number 88881.030454/2013-01 from the program CSF-PVE
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Phase portrait ; Poincaré disk ; Polynomial vector field ; Uniform isochronous center
Published in:	Discrete and continuous dynamical systems. Series B, Vol. 21 Núm. 1 (2016) , p. 121-131, ISSN 1553-524X

DOI: 10.3934/dcdsb.2016.21.121

Postprint 13 p, 310.1 KB

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