Abstract

We will present some results about the number of zeroes of the abelian integral associated to the system x'= y K(x,y)+ e P(x,y), y'=-x K(x,y)+ e Q(x,y), when K(x,y)=0 represents a set of k isolated points and P and Q are polynomials of degree n. We study also how these numbers changes moving the points.

This is a joint work with Joan Torregrosa.