Abelian integrals for polynomials with trivial global monodromy on ${\mathbb{C}}^2$

Jesús Muciño-Raymundo, Salomón Rebollo-Perdomo

We consider infinitesimal perturbations of Hamiltonian differential equations $dH+\epsilon \omega =0$ on the complex plane ${\mathbb{C}}^2$, where $H$ is a polynomial of degree $m+1$…