Viêt-Anh Nguyên Algebraic degrees for iterates of meromorphic self-maps of \(\mathbb P^k\). (English) Zbl 1112.37035 Publ. Mat., Barc. 50, No. 2, 457-473 (2006). 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. Cited in 11 Documents 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 Keywords:quasi-algebraically stable meromorphic maps; recurrent property; first dynamical degrees PDFBibTeX XMLCite \textit{Viêt-Anh Nguyên}, Publ. Mat., Barc. 50, No. 2, 457--473 (2006; Zbl 1112.37035) Full Text: DOI arXiv EuDML