Highest weak focus order for trigonometric Liénard equations
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Giné, Jaume (Universitat de Lleida. Departament de Matemàtica)
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)

Date:	2019
Abstract:	Given a planar analytic differential equation with a critical point which is a weak focus of order k, it is well known that at most k limit cycles can bifurcate from it. Moreover, in case of analytic Liénard differential equations this order can be computed as one half of the multiplicity of an associated planar analytic map. By using this approach, we can give an upper bound of the maximum order of the weak focus of pure trigonometric Liénard equations only in terms of the degrees of the involved trigonometric polynomials. Our result extends to this trigonometric Liénard case a similar result known for polynomial Liénard equations.
Grants:	Ministerio de Ciencia e Innovación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 Ministerio de Economía y Competitividad MTM2017-84383-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1276
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Trigonometric Liénard equation ; Weak focus ; Cyclicity
Published in:	Annali di Matematica Pura ed Applicata, vol. 199 (November 2019) p. 1673-1684, ISSN 1618-1891

DOI: 10.1007/s10231-019-00936-8

Post-print 12 p, 673.9 KB

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