This paper deals with small perturbations of a class of hyperelliptic Hamiltonian system, which is a Liénard system of the form ẋ = y, ẏ = Q1(x)+ εyQ2(x) with Q1 and Q2 polynomials of degree 4 and 3,… (More)

In this paper we consider the bifurcation of limit cycles of the system ˙ x = y(x 2 − a 2)(y 2 − b 2) + εP(x, y), ˙ y = −x(x 2 − a 2)(y 2 − b 2) + εQ (x, y) for ε sufficiently small, where a, b ∈ R −… (More)

We consider number of limit cycles of perturbed quintic Hamiltonian system with perturbation in the form of (2n+2m) or (2n+2m+1) degree polynomials. We show that the perturbed system has at most n +… (More)

In this paper we consider the number of isolated zeros of Abelian integrals associated to the perturbed system ẋ = y, ẏ = −x3(x− 1)2 + ε(α + βx + γx3)y, where ε > 0 is small and α, β, γ ∈ R. The… (More)