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| RANDOM ITERATION OF HOLOMOEPHIC SELF-MAPS OVER BOUNDED DOMAINS IN CN |
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Citation： |
Zhang Wenjun,Ren Fuyao.RANDOM ITERATION OF HOLOMOEPHIC SELF-MAPS OVER BOUNDED DOMAINS IN CN[J].Chinese Annals of Mathematics B,1995,16(1):33~42 |
| Page view： 1041
Net amount： 705 |
Authors： |
Zhang Wenjun; Ren Fuyao |
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| Abstract： |
This paper studies the asymptotic properties of the random iterations of both the form $G_n=f_1 \circ f_2 \circ \cdots \circ f_n$ and the form $F_n=f_n \circ f_{n-1} \circ \cdots \circ f_1$, where ${f_n} \subset H(\omega ,\omega)$ and $\omega \subset C^N$ is a bounded domain. It is found that, under some conditions, $G_n$ or $F_n$ tends to a point in $\overline{\omega}$ as $n\rightarrow \infty$. Some examples are also given to show that the conditions that we have given can ndt be dropped in general.Moreover, a complete description is given for $F_n$ or $G_n$ to tend to a point in $\omega$ under the condition $f_n \rightarrow f$. |
Keywords： |
Random iteration, Holomorphic map, Kobayashi metric. |
Classification： |
32h02,32H50. |
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