TY - JOUR
T1 - On the number of zeros of Abelian integrals for a kind of quartic Hamiltonians
AU - Wu, Juanjuan
AU - Zhang, Yongkang
AU - Li, Cuiping
PY - 2014/2/1
Y1 - 2014/2/1
N2 - An explicit upper bound B(n) is derived for the number of zeros of Abelian integrals I(h)=Γhg(x,y)dx-f(x,y)dy on the open interval (0,1/4), where Γh is an oval lying on the algebraic curve H(x,y)=x2+y2-x4+ax2 y2+y4 with a>-2,f(x,y) and g(x,y) are polynomials in x and y of degrees not exceeding n. Assume I(h) not vanish identically, then B(n)≤3n-14+12n-34+23.
AB - An explicit upper bound B(n) is derived for the number of zeros of Abelian integrals I(h)=Γhg(x,y)dx-f(x,y)dy on the open interval (0,1/4), where Γh is an oval lying on the algebraic curve H(x,y)=x2+y2-x4+ax2 y2+y4 with a>-2,f(x,y) and g(x,y) are polynomials in x and y of degrees not exceeding n. Assume I(h) not vanish identically, then B(n)≤3n-14+12n-34+23.
KW - Abelian integrals
KW - Poincare bifurcation
KW - Quartic Hamiltonian
KW - Weakened Hilbert 16th problem
UR - https://www.scopus.com/pages/publications/84891081807
U2 - 10.1016/j.amc.2013.11.092
DO - 10.1016/j.amc.2013.11.092
M3 - 文章
AN - SCOPUS:84891081807
SN - 0096-3003
VL - 228
SP - 329
EP - 335
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -