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:\[x' = 4y\left(abx^2-by^2+1\right)+\varepsilon x\left(ux^n+vy^n-b\frac{\beta+1}{\mu+1}x^\mu y^\beta-ux^2-\lambda\right)\]\[y' = 4x\left(ax^2-aby^2-1\right)+\varepsilon y\left(ux^n+vy^n+bx^\mu y^\beta-vy^2-\lambda\right)\]where \(\mu+\beta=n\), \(0