Iterates of holomorphic self-maps on pseudoconvex domains of finite and infinite type in \(\mathbb C^n\) (Q2827369)

The famous Wolff-Denjoy theorem [\textit{J. Wolff}, C. R. Acad. Sci., Paris 182, 200--201 (1926; JFM 52.0309.03); \textit{A. Denjoy}, C. R. Acad. Sci., Paris 182, 255--257 (1926; JFM 52.0309.04)] states that if a holomorphic self-map of the unit disk has no fixed points, then its iterations converge to a constant map of the disk to a point on its boundary. The result was extended to various classes of pseudoconvex domains in \({\mathbb C}^n \) such as strongly pseudoconvex domains and pseudoconvex domains of strictly finite type in the sense of Range. The authors prove a Wolff-Denjoy-type theorem for a large class of bounded pseudoconvex domains with smooth boundary in \({\mathbb C}^n \) that includes many domains of both finite and infinite type. The key property of such domains is the \(f\)-property from [the first author, J. Geom. Anal. 26, No. 1, 616--629 (2016; Zbl 1337.32024)].