Ritt's theorem and the Heins map in hyperbolic complex manifolds
Complex Variables
2015-06-26 v1 Dynamical Systems
Abstract
Let X be a Kobayashi hyperbolic complex manifold, and assume that X does not contain compact complex submanifolds of positive dimension (e.g., X Stein). We shall prove the following generalization of Ritt's theorem: every holomorphic self-map f of X such that f(X) is relatively compact in X has a unique fixed point p(f) in X, which is attracting. Furthermore, we shall prove that p(f) depends holomorphically on f in a suitable sense, generalizing results by Heins, Joseph-Kwack and the second author.
Cite
@article{arxiv.math/0411086,
title = {Ritt's theorem and the Heins map in hyperbolic complex manifolds},
author = {Marco Abate and Filippo Bracci},
journal= {arXiv preprint arXiv:math/0411086},
year = {2015}
}
Comments
5 pages; submitted to Proceedings of 2004 Beijing International Conference on Several Complex Variables