Dynamics of generic endomorphisms of Oka-Stein manifolds (Q2114154)

This paper is the third of a series in which the authors discuss the dynamic of an automorphism of a Oka-Stein manifold [the authors, Ann. Mat. Pura Appl. (4) 199, No. 4, 1697--1711 (2020; Zbl 1442.32028); J. Geom. Anal. 29, No. 2, 1744--1762 (2019; Zbl 1435.32025)]. In this work, they give many characterizations of the Fatou and Julia sets of a generic endomorphism of an Oka-Stein manifold \(X\). All the results are described in Theorem 1 in which, in particular, a generic endomorphism \(f\) of \(X\) is given, they state that, each periodic point is in fact hyperbolic; the Fatou and Julia sets are completerly invariant; \(f\) is chaotic on the Julia set and the iterates of \(f\) have the same Fatou and Julia sets of \(f\) itself.