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Iteration of analytic Euclidean contractions. (English) Zbl 0868.30027
Ali, Rosihan M. (ed.) et al., Computational methods and function theory 1994. Proceedings of the conference, Penang, Malaysia, March 21–25, 1994. Singapore: World Scientific. Ser. Approx. Decompos. 5, 57-74 (1995).
Summary: Let D be a bounded convex domain and suppose that f is an analytic map of D into itself with |f ' |<1. Then the diameter of f n (D) converges to zero and we obtain upper and lower estimates on the rate of this convergence. The methods used also give results in other circumstances; for example, for contractions of a domain in the n-dimensional Euclidean space.
MSC:
30D05Functional equations in the complex domain, iteration and composition of analytic functions
37F99Complex dynamical systems