20.500.12556/DiRROS-21154 Backward dynamics of non-expanding maps in Gromov hyperbolic metric spaces We study the interplay between the backward dynamics of a non-expanding self-map $f$ of a proper geodesic Gromov hyperbolic metric space $X$ and the boundary regular fixed points of $f$ in the Gromov boundary. To do so, we introduce the notion of stable dilation at a boundary regular fixed point of the Gromov boundary, whose value is related to the dynamical behaviour of the fixed point. This theory applies in particular to holomorphic self-maps of bounded domains $\Omega \subset\subset \mathbb{C}^q$, where $\Omega$ is either strongly pseudoconvex, convex finite type, or pseudoconvex finite type with $q=2$, and solves several open problems from the literature. We extend results of holomorphic self-maps of the disc $\mathbb{D}\subset \mathbb{C}$ obtained by Bracci and Poggi-Corradini. In particular, with our geometric approach we are able to answer a question, open even for the unit ball $\mathbb{B}^q\subset \mathbb{C}^q$, namely that for holomorphic parabolic self-maps any escaping backward orbit with bounded step always converges to a point in the boundary. holomorphic dynamics non-expanding maps Gromov hyperbolicity horofunctions boundary fixed points true false true Angleški jezik Ni določen Neznano 2025-01-08 12:52:26 2025-01-08 12:52:26 2025-01-09 03:38:02 0000-00-00 00:00:00 2024 0 0 39 str. article no. 109484 Vol. 439 Mar. 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2024-03-01 517.5 0001-8708 10.1016/j.aim.2023.109484 220693251 1-s2.0-S0001870823006278-main-1.pdf 1-s2.0-S0001870823006278-main-1.pdf 1 B26AAC59D66B58FE8805453A8683FEB6 636bc3e9f5f30055a000226c8f9d7dfcd54d69a1fa3dd20412df716a9610f779 f93e94e1-cdb7-11ef-ba3f-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=30008 https://www.sciencedirect.com/science/article/pii/S0001870823006278 1 08ef02cb-cdb7-11ef-ba3f-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=30007 Inštitut za matematiko, fiziko in mehaniko 0 0 0