ANALYSIS OF A PERTURBED HAMILTONIAN SYSTEM - Tigan, Gheorghe (Matematichki Bilten, 2005)
In this paper we study the existence, number and distribution of limit cycles of the perturbed Hamiltonian system given by: \[ x’ = 4y(abx^2-by^2+1) +ε x( ux^n+vy^n -bβ+1μ+1x^μ y^β -ux^2-λ ) \] \[ y’ = 4x(ax^2-aby^2-1) +ε y( ux^n+vy^n +bx^μ y^β -vy^2-λ ) \] where \(μ+β=n\), \(0<a<b<1\), \(0<ε1\), \(u,v,λ\) are the real parameters and \(n=2k\), \(k\) integer positive. Abelian integral method is employed, [15]. For some particular parameters we draw the distribution limit cycle diagrams.