Common fixed points of commuting holomorphic maps in the unit ball of
Authors:
Filippo Bracci
Affiliation:
Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, Via Belzoni 7, 35131 Padova, Italia
Abstract:
Let be the unit ball of (). We prove that if are holomorphic self-maps of such that , then and have a common fixed point (possibly at the boundary, in the sense of -limits). Furthermore, if and have no fixed points in , then they have the same Wolff point, unless the restrictions of and to the one-dimensional complex affine subset of determined by the Wolff points of and are commuting hyperbolic automorphisms of that subset.