The cyclicity of the period annulus of a reversible quadratic system
Liu, Changjian (Sun Yat-sen University. School of Mathematics (China))
Li, Chengzhi (Peking University. School of Mathematical Sciences (China))
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2021
Abstract:	We prove that perturbing the periodic annulus of the reversible quadratic polynomial differential system x˙ = y + ax2, y˙ = −x with a ≠ 0 inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycle, including their multiplicities. Since the first integral of the unperturbed system contains an exponential function, the traditional methods can not be applied, except in [6] a computer-assisted method was used. In this paper we provide a method for studying the problem. This is also the first purely mathematical proof of the conjecture formulated by F. Dumortier and R. Roussarie in [5] for q ≤ 2. The method may be used in other problems.
Grants:	Ministerio de Economía y Competitividad MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Perturbation of quadratic reversible center ; Abelian integral ; Limit cycle
Published in:	Proceedings of the Royal Society of Edinburgh Section A: Mathematics, (February 2021) , ISSN 1473-7124

DOI: 10.1017/prm.2021.2

Postprint 12 p, 322.1 KB

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