Random holomorphic iterations and degenerate subdomains of the unit disk

Authors:
Linda Keen and Nikola Lakic

Journal:
Proc. Amer. Math. Soc. **134** (2006), 371-378

MSC (2000):
Primary 32G15; Secondary 30C60, 30C70, 30C75

DOI:
https://doi.org/10.1090/S0002-9939-05-08280-8

Published electronically:
August 25, 2005

MathSciNet review:
2176004

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a random sequence of holomorphic maps of the unit disk to a subdomain , we consider the compositions

The sequence is called the

*iterated function system*coming from the sequence We prove that a sufficient condition on the domain for all limit functions of any to be constant is also necessary. We prove that the condition is a quasiconformal invariant. Finally, we address the question of uniqueness of limit functions.

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Additional Information

**Linda Keen**

Affiliation:
Department of Mathematics, Lehman College and Graduate Center, CUNY, Bronx, New York 10468

Email:
linda.keen@lehman.cuny.edu

**Nikola Lakic**

Affiliation:
Department of Mathematics, Lehman College and Graduate Center, CUNY, Bronx, New York 10468

Email:
nikola.lakic@lehman.cuny.edu

DOI:
https://doi.org/10.1090/S0002-9939-05-08280-8

Received by editor(s):
March 8, 2004

Published electronically:
August 25, 2005

Additional Notes:
The first author was partially supported by a PSC-CUNY Grant

The second author was partially supported by NSF grant DMS 0200733

Communicated by:
Juha M. Heinonen

Article copyright:
© Copyright 2005
American Mathematical Society