×

Iteration of contractions and analytic maps. (English) Zbl 0662.30017

The Denjoy-Wolff theorem states that if f is an analytic map of the unit disc into itself, then the iterates \(f^ n\) converge to some point in the closure of the unit disc. Excluding Möbius maps, each f is a contraction with respect to the hyperbolic metric. The result is generalized to contractions of Hadamard and visibility n-dimensional manifolds.
Reviewer: A.F.Beardon

MSC:

30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
51M10 Hyperbolic and elliptic geometries (general) and generalizations
51H20 Topological geometries on manifolds
PDFBibTeX XMLCite
Full Text: DOI