New lower bounds for the Hilbert numbers using reversible centers

Rafel Prohens, Joan Torregrosa

Producció científica: Contribució a revistaArticleRecercaAvaluat per experts

23 Cites (Scopus)

Resum

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.
Idioma originalAnglès
Pàgines (de-a)0331-355
Nombre de pàgines25
RevistaNonlinearity
Volum32
Número1
DOIs
Estat de la publicacióEn premsa - 2019

Fingerprint

Navegar pels temes de recerca de 'New lower bounds for the Hilbert numbers using reversible centers'. Junts formen un fingerprint únic.

Com citar-ho