A Fatou–Bieberbach domain in \mathbb C2\mathbb {C}^2 which is not Runge

Abstract  Since a paper by Rosay and Rudin (Trans. Am. Math. Soc. 310, 47–86, 1988) there has been an open question whether all Fatou–Bieberbach domains are Runge. We give an example of a Fatou–Bieberbach domain Ω in which is not Runge. The domain Ω provides (yet) a negative answer to a problem of Bremermann.