Annales Academić Scientiarum Fennicć
Mathematica
Volumen 32, 2007, 73-82

ACCUMULATION CONSTANTS OF ITERATED FUNCTION SYSTEMS WITH BLOCH TARGET DOMAINS

Linda Keen and Nikola Lakic

Department of Mathematics, Lehman College and Graduate Center, CUNY
Bronx, NY 10468, U.S.A; linda.keen 'at' lehman.cuny.edu

Department of Mathematics, Lehman College and Graduate Center, CUNY
Bronx, NY 10468, U.S.A.; nikola.lakic 'at' lehman.cuny.edu

Abstract. Given a random sequence of holomorphic maps f₁,f₂,f₃,... from the unit disk \Delta to a subdomain X, we consider the compositions

F_n = f₁ o f₂ o ... o f_{n - 1} o f_n.

The sequence {F_n}$ is called the iterated function system coming from the sequence f₁,f₂,f₃,... . We ask what points in X or \partial X can occur as limits. Our main result is that for a non-relatively compact Bloch domain X, any finite set of distinct points in X can be realized as the full set of limits of an IFS.

2000 Mathematics Subject Classification: Primary 32G15; Secondary 30C60, 30C70, 30C75.

Key words: Holomorphic dynamics, random iteration, iterated function systems, Bloch domains.

Reference to this article: L. Keen and N. Lakic: Accumulation constants of iterated function systems with Bloch target domains. Ann. Acad. Sci. Fenn. Math. 32 (2007), 73-82.

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