Abstract

We deal with polynomial vector fields $X\; =\; (P$₁,...,P_d) in $Cd$ with $d>1$. Let $m$_k be the degree of $P$_k. We call $(m$₁,...,m_k) the degree of $X$. We provide the best upper bounds for the polynomial vector field $X$ in function of its degree $(m$₁,...,m_k) of:
(1)the maximal number of invariant hyperplanes,
(2)the maximal number of parallel invariant hyperplanes, and
(3)the maximal number of invariant hyperplanes that pass through a single point.
Of couse we assume that the number of invariant hyperplanes is finite.

This is a joint work with Joao Carlos Medrado.