Bifurcations of limit cycles from cubic Hamiltonian systems with a center and a homoclinic saddle-loop.
Zhao, Yulin ; Zhang, Zhifen
Publicacions Matemàtiques, Tome 44 (2000), p. 205-235 / Harvested from Biblioteca Digital de Matemáticas
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It is proved in this paper that the maximum number of limit cycles of system

⎧ dx/dt = y

⎨

⎩ dy/dt = kx - (k + 1)x2 + x3 + ε(α + βx + γx2)y

is equal to two in the finite plane, where k > (11 + √33) / 4 , 0 < |ε| << 1, |α| + |β| + |γ| ≠ 0. This is partial answer to the seventh question in [2], posed by Arnold.

Publié le : 2000-01-01
DMLE-ID : 3915 
@article{urn:eudml:doc:41390,
     title = {Bifurcations of limit cycles from cubic Hamiltonian systems with a center and a homoclinic saddle-loop.},
     journal = {Publicacions Matem\`atiques},
     volume = {44},
     year = {2000},
     pages = {205-235},
     mrnumber = {MR1775762},
     zbl = {0962.34026},
     language = {en},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41390}
}

Zhao, Yulin; Zhang, Zhifen. Bifurcations of limit cycles from cubic Hamiltonian systems with a center and a homoclinic saddle-loop.. Publicacions Matemàtiques, Tome 44 (2000) pp. 205-235. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41390/