Julia Sets with a Wandering Branching Point

According to the Thurston No Wandering Triangle Theorem, a branching point in a locally connected quadratic Julia set is either preperiodic or precritical. Blokh and Oversteegen proved that this theorem does not hold for higher-degree Julia sets: there exist cubic polynomials whose Julia set is a locally connected dendrite with a branching point which is neither preperiodic nor precritical. In this article, we re-prove this result, constructing such cubic polynomials as limits of cubic polynomials for which one critical point eventually maps to the other critical point, which eventually maps to a repelling fixed point.