Things that evolve over time, can sometimes be described with differential equations or difference equations.
The field of Mathematics dedicated to the study of these equations
is called dynamical systems.
It is in this field Christian spends most of his time.

More specifically he looks at what happens when you apply the same mapping again and again, that is, iterate a mapping f.
If you think about this, and the mapping in question is analytic, you are actually in Holomorphic Dynamics.

Herman rings

Herman rings are interesting objects, which are studied in
holomorphic dynamics. A Herman ring is a doubly connected
maximal domain on which the dynamics are conjugate to an irrational
rotation. The animation shows what happens if we change the complex
structure such that the inner boundary is rotated with respect to
the outer.

Click on the animation to
the right to see more animations with a short
description.

Applied Mathematics

Christian has also dabbled in applied mathematics.

A picture can give another handle to grasp a mathematical object.
Often are geometric intution can lead us to results that would otherwise have escaped us.

I've written a little app, CHPlane, for investigating
the dynamics of 2D continuous time systems.