Center conditions for a class of planar rigid polynomial differential systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Rabanal, Roland (Pontificia Universidad Católica del Perú. Departamento de Ciencias)

Additional title:	Explicit focal basis for some planar rigid polynomial differential systems
Date:	2015
Abstract:	In general the center-focus problem cannot be solved, but in the case that the singularity has purely imaginary eigenvalues there are algorithms to solving it. The present paper implements one of these algorithms for the polynomial differential systems of the form x = -y + xf (x)g(y), y = x + yf (x)g(y), where f (x) and g(y) are arbitrary polynomials. These differential systems have constant angular speed and are also called rigid systems. More precisely, this paper gives focal bases of these systems, and then necessary and sufficient conditions in order to have an uniform isochronous center. In particular, the existence of a focus with the highest order is also studied.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-410 European Commission 316338 European Commission 318999
Note:	El títol de la versió pre-print de l'article és: Explicit focal basis for some planar rigid polynomial differential systems
Note:	Agraïments: The first author was partially partially supported by CAPES/DGU grant number BEX 12566/12-8.
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Focal basis ; Isochronous center ; Limit cycles ; Lyapunov quantities ; The center problem
Published in:	Discrete and continuous dynamical systems. Series A, Vol. 35 Núm. 3 (2015) , p. 1075-1090, ISSN 1553-5231

DOI: 10.3934/dcds.2015.35.1075

Postprint 18 p, 697.9 KB

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