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

Finiteness of commutable maps of bounded degree