Global phase portraits of quadratic systems with an ellipse and a straight line as invariant algebraic curves
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Yu, Jiang (Shanghai Jiao Tong University. Department of Mathematics)

Date:	2015
Abstract:	In this article we study a class of integrable quadratic systems and classify all its phase portraits. More precisely, we characterize the class of all quadratic polynomial differential systems in the plane having an ellipse and a straight line as invariant algebraic curves. We show that this class is integrable and we provide all the different topological phase portraits that this class exhibits in the Poincaré disc.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 318999 European Commission 316338
Note:	Agraïments/Ajudes: the grant UNAB13-4E-1604, and from the recruitment program of high-end foreign experts of China. The second author is partially supported by the state key program of NNSF of China grant number 11431008, NSF of Shanghai grant number 15ZR1423700 and NSF of Jiangsu, BK 20131285.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	First integral ; Global phase portraits ; Invariant ellipse ; Invariant straight line ; Quadratic system
Published in:	Electronic journal of differential equations, Vol. 314 (2015) , p. 1-14, ISSN 1072-6691

Postprint 17 p, 401.0 KB

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