Abstract:

We study the set of periods of the homogeneous polynomial maps $f:mathbb{R}^n ightarrow mathbb{R}^n$ and $f: mathbb{C}^n ightarrow mathbb{C}^n$ 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.

This is a joint work with Violetta Pilyugina.