New lower bounds for the Hilbert numbers using reversible centers
Prohens, Rafel (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2019
Abstract:	In this paper we provide the best lower bounds, that are known up to now, for the Hilbert numbers of polynomial vector fields of degree N,, for small values of N. These limit cycles appear bifurcating from symmetric Darboux reversible centers with very high simultaneous cyclicity. The considered systems have, at least, three centers, one on the reversibility straight line and two symmetric outside it. More concretely, the limit cycles are in a three nests configuration and the total number of limit cycles is at least 2n + m, for some values of n and m. The new lower bounds are obtained using simultaneous degenerate Hopf bifurcations. In particular, H(4) ≥ 28, H(5) ≥ 37, H(6) ≥ 53, H(7) ≥ 74, H(8) ≥ 96, H(9) ≥ 120 and H(10) ≥ 142.
Grants:	Ministerio de Economía y Competitividad MTM2013-40998-P Ministerio de Economía y Competitividad MTM2014-54275-P Ministerio de Economía y Competitividad MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568
Note:	Altres ajuts: UNAB13-4E-1604 (FEDER)
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Published in:	Nonlinearity, Vol. 32, Núm. 1 (January 2019) , p. 331-355, ISSN 1361-6544

DOI: 10.1088/1361-6544/aae94d

Postprint 26 p, 414.4 KB

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