After a review of previous results, we prove the following theorem: Let D be a strictly linearly convex domain with C^3 boundary. Let f, g : D → D be holomorphic maps without fixed points in D such that f ◦ g= g ◦ f . Then f and g have the same Wolff point, unless their restrictions to the unique (up to parametrization) complex geodesic whose closure contains the Wolff points of f and g , are two commuting (hyperbolic) automorphisms of such a geodesic.
Mappe Olomorfe che Commutano / Filippo Bracci. - STAMPA. - 12:(2000), pp. 1-35. ( Seminari di Geometria).
Mappe Olomorfe che Commutano
Filippo Bracci
2000
Abstract
After a review of previous results, we prove the following theorem: Let D be a strictly linearly convex domain with C^3 boundary. Let f, g : D → D be holomorphic maps without fixed points in D such that f ◦ g= g ◦ f . Then f and g have the same Wolff point, unless their restrictions to the unique (up to parametrization) complex geodesic whose closure contains the Wolff points of f and g , are two commuting (hyperbolic) automorphisms of such a geodesic.
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