Annales Academię Scientiarum Fennicę

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
*f*_{1},*f*_{2},*f*_{3},...
from the unit disk \Delta
to a subdomain *X*, we consider the compositions

*F*_{n} = *f*_{1} o *f*_{2}
o ... o *f*_{n - 1} o *f*_{n}.
The sequence {*F*_{n}}$ is called the *iterated
function system* coming from the sequence
*f*_{1},*f*_{2},*f*_{3},... .
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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Copyright © 2007 by Academia Scientiarum Fennica