Polynomial Homogeneous Maps and Their Periods

Abstract

We study the set of periods of the homogeneous polynomial maps $f:\mathbb{R}^n → \mathbb{R}^n$ and $f : \mathbb{C}^n → \mathbb{C}^n$ of degree $m > 1.$ For these complex maps, we also describe the number of invariant straight lines through the origin by $f^k$ for $k = 1, 2, . . .$ and the dynamics of $f^k$ over them.