Nilpotence of Orbits under Monodromy and the Length of Melnikov Functions

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

Let $F\in \mathbb{C}[x,y]$ be a polynomial, $\gamma (z)\in {\pi }_1(F^{-1}(z))$ a non-trivial cycle in a generic fiber of $F$ and let $\omega$ be a polynomial $1$-form, thus defining a polynomial d…