Bifurcations of limit cycles from cubic Hamiltonian systems with a center and a homoclinic saddle-loop

Autores: Zhifen Zhang, Yulin Zhao
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 44, Nº 1, 2000, págs. 205-235
Idioma: inglés
DOI: 10.5565/publmat_44100_08
Títulos paralelos:
- Bifurcaciones de ciclos límite a partir de sistemas hamiltonianos cúbicos con un centro y un ciclo silla homoclínico
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Resumen
- It is proved in this paper that the maximum number of limit cycles of system \[ \begin{cases} \frac{dx}{dt}=y,\\ \frac{dy}{dt}=kx-(k+1)x^2+x^3+\epsilon(\alpha+\beta x+\gamma x^2)y \end{cases} \] is equal to two in the finite plane, where $k>\frac{11+\sqrt{33}}{4}$, $0<|\epsilon|\ll1$, $|\alpha|+|\beta|+|\gamma|\ne 0$. This is partial answer to the seventh question in [2], posed by Arnold.