Beardon, A. F. Iteration of contractions and analytic maps. (English) Zbl 0662.30017 J. Lond. Math. Soc., II. Ser. 41, No. 1, 141-150 (1990). 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 Cited in 1 ReviewCited in 22 Documents 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 Keywords:visibility manifolds; Hadamard manifolds; Schwarz lemma; hyperbolic metric PDFBibTeX XMLCite \textit{A. F. Beardon}, J. Lond. Math. Soc., II. Ser. 41, No. 1, 141--150 (1990; Zbl 0662.30017) Full Text: DOI