  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.
