Noetherianity and length of Melnikov functions

Pavao Mardesic, Dmitry Novikov, Laura Ortiz-Bobadilla +1

We study foliations in ${\mathbb{C}}^2$ given by polynomial deformations of the form $dH+\hat{I}\mu \hat{I}\cdot =0$, with ${\hat{I}}^3(t)\subset H^{-1}(t)$ a family of cycles. The \emph{Poincaré first return m…