**Adrian Jenkins**

Iowa State University, USA

March 15, 2012

**Local Non-Archimedean Dynamical Systems in Two Variables**:
In joint work with Steven Spallone, we consider locally-convergent
analytic mappings over K^{2}, where K is a non-archimedean field.
Our goal is to construct conjugations to polynomial normal forms. In
particular, our focus is on so-called `Semi-hyperbolic' dynamical systems. We give a full formal and analytic classification, building off earlier formal work in the complex plane, and analytic work in the one-dimensional non-archimedean case. The results are in stark contrast to the complex case.