  In 2001 E. Ghys, X. Gomez-Mont and J. Saludes defined the Fatou and Julia
components of transversely holomorphic foliations on compact manifolds. It is a
partition of the manifold in two saturated sets: the Fatou set which represents
the non-chaotic part of the foliation and its complementary, the Julia set.
Using the Brownian motion transverse to the foliation, it is proved in this
paper that, if the foliation is taut and if F is a wandering component of the
Fatou set, then almost every point of the topological boundary of F (almost for
any harmonic measure on the boundary) is a limit point of each leaf of F.
