The Real Dynamics of Bieberbach's Example
Time and place
1 PM on Thursday, November 1st, 2012; NAC 6/113
Sandra Hayes (CCNY)
Abstract
Bieberbach constructed in 1933 domains in C^2 which were biholomorphic to C^2 but omitted an open set. The existence of such domains was unexpected, because the analogous statement for the one-dimensional complex plane is false. The special domains Bieberbach considered are given as basins of attraction of a cubic Henon map. This classical method of construction is one of the first applications of dynamical systems to complex analysis. In this talk the boundaries of the real sections of Bieberbach’s domains will be shown to be smooth. The real Julia sets of Bieberbach’s map will be calculated explicitly and illustrated with computer generated graphics.
