turkmath.org

The main purpose of this talk is to give an introduction to the eld of holomorphic dynamics - which can be described as the study of long-term behavior of holomorphic maps under iteration. The concept of holomorphic motion plays an important role in the study of parameter spaces. We will pay particular attention to the case of holomorphic motions parametrized by the punctured disk. We will study the extension properties of such motions, and the associated what we call \holomorphic explosions." We illustrate these ideas with an example from transcendental dynamics.