2013/11/09 by Nicolas Hussenot, Hussenot, Nicolas
Mathematics · #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CV #math.DS
paper · pdf · doi:10.48550/arxiv.1311.2218
arxiv created 2015/08/25 · arxiv updated 2015/08/26
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.