Algebraic degrees for iterates of meromorphic self-maps of ${\P }^k$

Abstract

We first introduce the class of quasi-algebraically stable meromorphic maps of ${\P }^k.$ This class is strictly larger than that of algebraically stable meromorphic self-maps of ${\P }^k.$ 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.

14 pages. To appear in ``Publicacions Matematiques"

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