Iteration of Some Birational Polynomial Maps in Pn2

Abstract

Iteration theory of birational maps in the two dimensional complex projective space P 2 was developed mainly by Diller [1] and Nishimura [2]. Diller was inspired by works done for polynomial automorphisms of C 2, and he applied pluripotential theory to iteration theory of birational maps. On the other hand, Nishimura classified birational maps in P 2 of the form F +: [z : w : t] ↦ [f 0 : f l : t 2], where f 0, f 1 are homogeneous polynomials of degree 2. Up to a suitable conjugation of PGL(P 2), his classification table can be written as follows: