Fatou–Bieberbach domain

A Fatou - Bieberbach domain is a real branch of which is biholomorphic equivalent, ie an open is called Fatou - Bieberbach area if there is a bijective holomorphic function and a holomorphic inverse function.

History

As a consequence of the Riemann mapping theorem there is no Fatou - Bieberbach areas in the case. In higher dimensions Fatou - Bieberbach areas were first discovered in the 1920s by Pierre Fatou and Ludwig Bieberbach and later named after their discoverers. Since the 1980s, Fatou - Bieberbach areas are again a subject of mathematical research.

Swell

• Pierre Fatou: Sur les fonctions de deux méromorphes variable, Sur certaines fonctions de deux uniform variable. Comptes rendus hebdomadaires of séances de l' Académie des sciences, Volume 175 (1922), pp. 862-865, 1030-1033.
• Ludwig Bieberbach: Example of two entire functions of two complex variables which mediate the volumtreue a simple illustration of a part of himself. Prussian Academy of Sciences. Meeting reports, 1933, pp. 476-479.
• J.-P. Rosay, W. Rudin: holomorphic maps from to. Transactions of the American Mathematical Society, Volume 310 (1988), Issue 1, pp. 47-86.

• Function theory