Random holomorphic iterations and degenerate subdomains of the unit disk
| dc.creator | Keen, Linda | |
| dc.creator | Lakic, Nikola | |
| dc.date | 2005-03-04 | |
| dc.date.accessioned | 2026-07-07T05:17:40Z | |
| dc.date.available | 2026-07-07T05:17:40Z | |
| dc.description | Given a random sequence of holomorphic maps $f_1,f_2,f_3,...$ of the unit disk $Δ$ to a subdomain $X$, we consider the compositions $$F_n=f_1 \circ f_{2} \circ ... f_{n-1} \circ f_n.$$ The sequence $\{F_n\}$ is called the {\em iterated function system} coming from the sequence $f_1,f_2,f_3,....$ We prove that a sufficient condition on the domain $X$ for all limit functions of any $\{F_n\}$ to be constant is also necessary. We prove the condition is a quasiconformal invariant. Finally, we address the question of uniqueness of limit functions. | |
| dc.description | 8 Pages To appear PAMS | |
| dc.identifier | https://arxiv.org/abs/math/0503079 | |
| dc.identifier | http://arxiv.org/abs/math/0503079 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74387 | |
| dc.subject | Complex Variables | |
| dc.subject | Dynamical Systems | |
| dc.subject | Primary 32G15; Secondary 30C60, 30C70 | |
| dc.title | Random holomorphic iterations and degenerate subdomains of the unit disk | |
| dc.type | text |