A Fatou-Bieberbach Domain with a Complex Line in the Boundary
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The purpose of this thesis is to construct a Fatou-Bieberbach domain in two complex variables with a complex line in the boundary. To achieve this, we will first explore the dynamics of an analytic transformation in one variable. Then we explore a Fatou-Bieberbach domain with a fixed point in its interior, because the procedure to show that this has the wanted properties is easier than for the one we plan to explore later. In the end, the principles for the simpler domain and the one variable dynamics are used to construct the wanted domain, and to show that it is indeed a Fatou Bieberbach domain.