A Fatou-Julia decomposition of transversally holomorphic foliations

On Fatou-Julia decompositions

“…It is apparent that restrictions of f belong to Γ × and that restrictions of g do not belong to ∆ × . On the other hand, pr 1 • f = g • pr 1 .…”

“…Here we present two examples of non-compactly generated psg's in advance. Fatou-Julia decompositions of these psg's are examined under a tentative definition in [1]. The decompositions are as follows under Definition 2.2.…”

“…Note that these psg's are generated by pseudogroups so that the -171 -conditions (wF) and (F) are equivalent. Results are the same as in [1] but we proceed by correcting typographic errors.…”

“…Iterations of rational mappings and actions of finitely generated Kleinian groups are typical holomorphic dynamical systems on CP 1 . The notion of the Julia sets [15], [16] and the limit sets [14] are significant in their study.…”

“…If foliations are given on closed manifolds, then the holonomy pseudogroups have certain compactness called 'compact generation'. The notion of the Julia sets is also known for complex codimension-one transversely holomorphic foliations of closed manifolds [6], [8], [1]. One of the aims of this article is to give a unified definition of these Julia sets and limit sets.…”