Attractive Holomorphic Limit Cycles - H. HOLMANN (Rendiconti di Matematica e delle Sue Applicazioni, 1995)
Holomorphic foliations on connected complex manifolds are studied as dynamical systems, notion like limit sets, limit cycles, basins of attraction, attractors being defined geometrically. Under the assumptions that there are only “few” compact leaves and that the space of the non-compact leaves is hausdorff, it is shown: each compact leaf is an almost global attractor; for each non-compact leaf F the number of connected components of its limit set is equal to the number of compact leaves, an upper bound of which is given by the number of ends of F. These results are interpreted especially for holomorphic C-actions.