Upper bounds for the number of zeroes for some Abelian integrals

Armengol Gasull, J. Tomás Lázaro, Joan Torregrosa

Consider the vector field $x^{\prime }=-yG(x,y),y^{\prime }=xG(x,y),$ where the set of critical points $\{G(x,y)=0\}$ is formed by $K$ straight lines, not passing through the origin and paral…