Fractal aspects of localization of algebraic integers and complex dynamical systems (Q921044)

\textit{P. Moussa}, \textit{J. S. Geronimo} and \textit{D. Bessis} [Sémin. Théor. Nombres, Univ. Bordeaux I. 1984/85, Exp. No.21 (1985; Zbl 0591.12002), see also C. R. Acad. Sci., Paris, Sér. I 299, 281-284 (1984; Zbl 0563.30018)] proved that the set of algebraic integers which, together with all their conjugates, lie in the filled-in Julia set K(P) of a monic polynomial P with integer coefficients, is the set of preperiodic points of P. The authors extend this result to monic polynomials with coefficients in the ring \(O_ F\) of algebraic integers in either \({\mathbb{Q}}\) or an imaginary quadratic field \({\mathbb{Q}}(\sqrt{-m})\). They list all such monic polynomials for which the filled-in Julia set is connected. There are further generalizations.