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Algebraic degrees for iterates of meromorphic self-maps of \(\mathbb P^k\). (English) Zbl 1112.37035

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

MSC:

37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
32H50 Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables
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