Limit cycles for a variant of a generalized Riccati equation
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemàtica)

Date:	2017
Abstract:	In this paper we provide a lower bound for the maximum number of limit cycles surrounding the origin of systems (x, y = x) given by a variant of the generalized Riccati equation \[ x x^2n 1 x b x^4n 3=0, \] where b>0, b \R, n is a non--negative integer and is a small parameter. The tool for proving this result uses Abelian integrals.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999 Ministerio de Economía y Competitividad MTM2013-40998-P
Note:	Agraïments: The second author is partially supported by FCT/Portugal through UID/MAT/04459/2013
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Abelian integrals ; Generalized Riccati system ; Limit cycles ; Weak 16th Hilbert problem
Published in:	Applied mathematics letters, Vol. 68 (2017) , p. 76-79, ISSN 0893-9659

DOI: 10.1016/j.aml.2016.11.016

Postprint 5 p, 726.8 KB

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