For a sequence (cn) of complex numbers, the quadratic polynomials $f_{c_n}:=z^2+c_n$ and the sequence (Fn) of iterates $F_n:=f_{c_n}\circ\dotsb \circ f_{c_1}$ are considered. The Fatou set $\mathcal{F}(c_n)$ is defined as the set of all $z\in \hat{\mathbb{C}}: =\mathbb{C}\cup \{\infty\}$ such that (Fn) is normal in some neighbourhood of z, while the complement $\mathcal{J}(c_n)$ of $\mathcal{F}(c_n)$ (in $\hat{\mathbb{C}}$) is called the Julia set. In this paper we discuss the conditions for $\mathcal{J}(c_n)$ to be totally disconnected. A problem posed by Brück is solved.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.