Finiteness of commutable maps of bounded degree
Bull. Korean Math. Soc. 2015 Vol. 52, No. 1, 45-56
https://doi.org/10.4134/BKMS.2015.52.1.45
Printed January 31, 2015
Chong Gyu Lee and Hexi Ye
Soongsil University, University of Toronto
Abstract : 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
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