Bulletin of the
Korean Mathematical Society BKMS

In this paper, we study the relation between two dynamical systems $(V,f)$ and $(V,g)$ with $f\circ g = g \circ f$. As an application, we show that an endomorphism (respectively a polynomial map with Zariski dense, of bounded $\Pre(f)$) has only finitely many endomorphisms (respectively polynomial maps) of bounded degree which are commutable with $f$.

Keywords: height, preperiodic point, endomorphism, polynomial map, dynamical system, commutable maps

MSC numbers: Primary 37P05, 37P35; Secondary 11C08, 37F10