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

Zhao, Yulin, and Zhang, Zhifen. "Bifurcations of limit cycles from cubic Hamiltonian systems with a center and a homoclinic saddle-loop.." Publicacions Matemàtiques 44.1 (2000): 205-235. <http://eudml.org/doc/41390>.

@article{Zhao2000,
abstract = {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)yis equal to two in the finite plane, where k &gt; (11 + √33) / 4 , 0 &lt; |ε| &lt;&lt; 1, |α| + |β| + |γ| ≠ 0. This is partial answer to the seventh question in [2], posed by Arnold.},
author = {Zhao, Yulin, Zhang, Zhifen},
journal = {Publicacions Matemàtiques},
keywords = {Sistema hamiltoniano; Sistemas diferenciales; Variedades; Ciclos límite; Perturbaciones; Integrales abelianas; limit cycles; Hilbert's 16th problem; cubic Hamiltonian systems},
language = {eng},
number = {1},
pages = {205-235},
title = {Bifurcations of limit cycles from cubic Hamiltonian systems with a center and a homoclinic saddle-loop.},
url = {http://eudml.org/doc/41390},
volume = {44},
year = {2000},
}

TY - JOUR
AU - Zhao, Yulin
AU - Zhang, Zhifen
TI - Bifurcations of limit cycles from cubic Hamiltonian systems with a center and a homoclinic saddle-loop.
JO - Publicacions Matemàtiques
PY - 2000
VL - 44
IS - 1
SP - 205
EP - 235
AB - 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)yis equal to two in the finite plane, where k &gt; (11 + √33) / 4 , 0 &lt; |ε| &lt;&lt; 1, |α| + |β| + |γ| ≠ 0. This is partial answer to the seventh question in [2], posed by Arnold.
LA - eng
KW - Sistema hamiltoniano; Sistemas diferenciales; Variedades; Ciclos límite; Perturbaciones; Integrales abelianas; limit cycles; Hilbert's 16th problem; cubic Hamiltonian systems
UR - http://eudml.org/doc/41390
ER -