On the Fatou–Julia decomposition of transversally holomorphic foliations of complex codimension one

Abstract

The Fatou–Julia decomposition of complex codimension-one foliations is given by Ghys, Gomez-Mont and Saludes. The Julia sets are expected to play a role of minimal sets of real codimension-one foliations. For example, it is known that the Godbillon–Vey class is trivial if the Julia set is empty. In this paper, we propose another decomposition obtained in a slightly different way and announce some results.