Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Messias, Marcelo (Universidade Estadual Paulista. Departamento de Matemática e Computação (Brazil))
Reinol, Alisson C. (Universidade Estadual Paulista. Departamento de Matemática e Computação (Brazil))

Date:	2017
Abstract:	In this paper, we give the normal form of all planar polynomial vector fields of degree d ≤ 3 having two nonconcentric circles C and C as invariant algebraic curves and the function H=C C , with α and β real values, as first integral. Moreover, we classify all global phase portraits on the Poincaré disc of a subclass of these vector fields.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014-SGR-568 European Commission 316338 European Commission 318999
Note:	Altres ajuts: ICREA Academia, FEDER-UNAB10-4E-378, CNPq-Brazil grant 308315/2012-0, FAPESP grant 12/18413-7 and FAPESP grant 2011/16154-1
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Quadratic and cubic vector fields ; Invariant algebraic curves ; Limit cycles ; Poincaré compactification ; Global analysis ; Normal forms
Published in:	Dynamical Systems, Vol. 32, Issue 3 (2017) , p. 374-390, ISSN 1468-9375

DOI: 10.1080/14689367.2016.1263600

Postprint 17 p, 570.2 KB

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