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 be a bounded convex domain and suppose that is an analytic map of into itself with . Then the diameter of 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 -dimensional Euclidean space.
|30D05||Functional equations in the complex domain, iteration and composition of analytic functions|
|37F99||Complex dynamical systems|