论文信息 - Thirteen limit cycles for a class of Hamiltonian systems under seven-order perturbed terms

Thirteen limit cycles for a class of Hamiltonian systems under seven-order perturbed terms

Abstract In this paper we study the existence, number and distribution of limit cycles of the perturbed Hamiltonian system: x ′ = 4 y ( abx 2 - by 2 + 1 ) + e x ux n + vy n - b β + 1 μ + 1 x μ y β - ux 2 - λ y ′ = 4 x ( ax 2 - aby 2 - 1 ) + e y ( ux n + vy n + bx μ y β - vy 2 - λ ) where μ + β = n , 0 a b e ≪ 1, u , v , λ are the real parameters and n = 2 k , 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.

Gheorghe Tigan | G. Tigan

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