ON INTERIOR POINTS OF THE JULIA SET J（R） FOR RANDOM DYNAMICAL SYSTEM R

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ON INTERIOR POINTS OF THE JULIA SET J(R) FOR RANDOM DYNAMICAL SYSTEM R

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.