Thirteen limit cycles for a class of Hamiltonian systems under seven-order perturbed terms
نویسنده
چکیده
In this paper we study the existence, number and distribution of limit cycles of the perturbed Hamiltonian system: 0960-0 doi:10 E-m x0 1⁄4 4yðabx by þ 1Þ þ ex ux þ vy b þ 1 l þ 1 x y ux k y0 1⁄4 4xðax aby 1Þ þ eyðux þ vy þ bxy vy kÞ where l + b = n, 0 < a < b < 1, 0 < e 1, u, v, k are the real parameters and n = 2k, k an integer positive. Applying the Abelian integral method [Blows TR, Perko LM. Bifurcation of limit cycles from centers and separatrix cycles of planar analytic systems. SIAM Rev 1994;36:341–76] in the case n = 6 we find that the system can have at least 13 limit cycles. Numerical explorations allow us to draw the distribution of limit cycles. 2005 Elsevier Ltd. All rights reserved.
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