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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. For the entire collection see [Zbl 0863.00033].

##### MSC:
 30D05 Functional equations in the complex domain, iteration and composition of analytic functions 37F99 Complex dynamical systems