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- W4307936592 abstract "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 $Omegasubsetsubset mathbb{C}^q$, 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 $mathbb{B}^qsubset mathbb{C}^q$, namely that for holomorphic parabolic self-maps any escaping backward orbit with bounded step always converges to a point in the boundary." @default.
- W4307936592 created "2022-11-06" @default.
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- W4307936592 date "2022-10-31" @default.
- W4307936592 modified "2023-09-27" @default.
- W4307936592 title "Backward dynamics of non-expanding maps in Gromov hyperbolic metric spaces" @default.
- W4307936592 doi "https://doi.org/10.48550/arxiv.2210.17480" @default.
- W4307936592 hasPublicationYear "2022" @default.
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