Finiteness of commutable maps of bounded degree

摘要

In this paper, we study the relation between two dynamical systems $(V,f)$ and $(V,g)$ with $fcirc g = g circ f$. 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 $f$.