A FATOU-JULIA DECOMPOSITION OF TRANSVERSALLY HOLOMORPHIC FOLIATIONS

作者：Asuke Taro^*

来源：Annales de l'Institut Fourier, 2010, 60(3): 1057-1104.

• Holomorphic foliations
• Fatou set
• Julia set
• Riemannian foliations

A Fatou-Julia decomposition of transversally holomorphic foliations of complex codimension one was given by Ghys, Gomez-Mont and Sa hides. In this paper, we propose another decomposition in terms of normal families. Two decompositions have common properties as well as certain differences. It will be shown that the Fatou sets in our sense always contain the Fatou sets in the sense of Ghys, Gomez-Mont and Saludes and the inclusion is strict in some examples. This property is important when discussing a version of Duminy's theorem in relation to secondary characteristic classes. The structure of Fatou sets is studied in detail, and some properties of Julia sets are discussed. Some similarities and differences between the Julia sets of foliations and those of mapping iterations will be shown. An application to the study of the transversal Kobayashi metrics is also given.

• 出版日期2010