Algebraic degrees for iterates of meromorphic self-maps of ¶^k

2006/03/22 by Viet-Anh Nguyen, Nguyen, Viet-Anh
Mathematics · #58F23 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #Primary 32F50 #Secondary 58F15 #math.AG #math.CV #msc:32F50 #msc:58F15 #msc:58F23

paper · pdf · doi:10.48550/arxiv.math/0603545

14 pages. To appear in ``Publicacions Matematiques"

arxiv created 2006/03/22 · arxiv updated 2009/12/01

Abstract

We first introduce the class of quasi-algebraically stable meromorphic maps of ¶^k. This class is strictly larger than that of algebraically stable meromorphic self-maps of ¶^k. Then we prove that all maps in the new class enjoy a recurrent property. In particular, the algebraic degrees for iterates of these maps can be computed and their first dynamical degrees are always algebraic integers.

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