Backward iteration in strongly convex domains
Complex Variables
2018-10-03 v2 Dynamical Systems
Abstract
We prove that a backward orbit with bounded Kobayashi step for a hyperbolic or strongly elliptic holomorphic self-map of a bounded strongly convex domain in the d-dimensional complex Euclidean space necessarily converges to a boundary fixed point, generalizing previous results obtained by Poggi-Corradini in the unit disk and by Ostapyuk in the unit ball.
Cite
@article{arxiv.1104.5370,
title = {Backward iteration in strongly convex domains},
author = {Marco Abate and Jasmin Raissy},
journal= {arXiv preprint arXiv:1104.5370},
year = {2018}
}
Comments
We have found a gap in the proofs of Lemmas 2.2 and 2.5 of the published version of this paper. Here we add to the previous version a note where we fill these gaps, giving a proof of the main results using different arguments. For the benefit of the reader, we report the complete proof of the main theorem, including the needed background results