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

Viet-Anh Nguyen
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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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Viet-Anh Nguyen. 2006-03-22. Algebraic degrees for iterates of meromorphic self-maps of $¶^k$. https://arxiv.org/abs/math/0603545

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