Density of backward paths on the Julia set of a semigroup - Chacón, Gerardo R.; Colucci, Renato; D’Angeli, Daniele (Sarajevo Journal of Mathematics, 2024)
A well-known result from the theory of dynamics of semigroups of rational functions is that the backward orbit of almost every complex number accumulates on the Julia set of the semigroup. In this article we signiﬁcantly improve that result by giving a tree structure to the backward orbit and showing that almost every path of the tree is dense in the Julia set of the semigroup.