Classification of Recurrent Domains for Holomorphic Maps on Complex Projective Spaces

摘要

We generalize the classification of recurrent domains for holomorphic maps on two-dimensional complex projective space given in Forn?ss and Sibony (Math. Ann. 301:813-820, 1995) to higher dimensions. In particular, we show that an invariant recurrent Fatou component is either an attracting basin or a Siegel domain or it retracts to a lower-dimensional Siegel manifold.