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

The leaves of the Fatou set accumulate on the leaves of the Julia set