Lower bounds for the local cyclicity for families of centers
Giné, Jaume (Universitat de Lleida. Departament de Matemàtica)
Gouveia, Luiz Fernando (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2021
Abstract:	In this paper we are interested on how the local cyclicity of a family of centers depends on the parameters. This fact, was pointed out in [21], to prove that there exists a family of cubic centers, labeled by CD12 31 in [25], with more local cyclicity than expected. In this family there is a special center such that at least twelve limit cycles of small amplitude bifurcate from the origin when we perturb it in the cubic polynomial general class. The original proof has some important gaps that we correct here. We take the advantage of better understanding of the bifurcation phenomenon in non generic cases to show two new cubic systems exhibiting 11 limit cycles and another exhibiting 12. Finally, using the same techniques, we study the local cyclicity of holomorfic quartic centers, proving that 21 limit cycles of small amplitude bifurcate from the origin, when we perturb in the class of quartic polynomial vector fields.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1276 Ministerio de Ciencia e Innovación MTM2017-84383-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 Ministerio de Ciencia e Innovación MTM2016-77278-P European Commission 777911
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Small-amplitude limit cycle ; Polynomial vector field ; Center cyclicity ; Lyapunov constants ; Higher order developments and parallelization
Published in:	Journal of differential equations, Vol. 275 (February 2021) , p. 309-331, ISSN 1090-2732

DOI: 10.1016/j.jde.2020.11.035

Postprint 21 p, 476.1 KB

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