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| ON INTERIOR POINTS OF THE JULIA SET J(R) FOR RANDOM DYNAMICAL SYSTEM R |
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Citation： |
Gong Zhimin,Ren Fuyao.ON INTERIOR POINTS OF THE JULIA SET J(R) FOR RANDOM DYNAMICAL SYSTEM R[J].Chinese Annals of Mathematics B,1997,18(4):503~512 |
| Page view： 967
Net amount： 706 |
Authors： |
Gong Zhimin; Ren Fuyao |
Foundation： |
the National Natural Science Foundation of China and by the Doctoral Program Foundation of the State Education Commission of China |
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| Abstract： |
The authors consider the random iteration of serval functions.
Denote by $ J(R) $ the Julia set for the random iteration dynamical system formed by a set of complex functions $R=\{R_1,R_2,\cdots,R_M\} $. Some sufficient conditions are given for $J(R)$ to have no interior points. Also some conditions are given for $J(R) $ to have interior points but fail to be the extended plane. In addition, $ J(az^n, bz^n)\ ( n\geq 2, ab\neq 0 ) $ and $ J(z^2+c_1, z^2+ c_2) $ are investigated and some interesting results are obtained. |
Keywords： |
Random iteration, Dynamical system, Julia set |
Classification： |
30D05 |
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