Connectedness of Julia sets for a quadratic random dynamical system

For a sequence (c(n)) of complex numbers, the quadratic polynomials f(cn) := z(2) + c(n) and the sequence (F-n) of iterates F-n := f(cn) circle...circle f(c1) are considered. The Fatou set F(c(n)) is defined as the set of all z is an element of (C) over cap := C boolean OR {infinity} such that (F-n) is normal in some neighbourhood of z, while the complement J(c(n)) of F(c(n)) (in (C) over cap) is called the Julia set. In this paper we discuss the conditions for J(c(n)) to be totally disconnected. A problem posed by Bruck is solved.