Local Non-Archimedean Dynamical Systems in Two Variables

by Prof. Adrian Jenkins (Iowa State University, USA)

Thursday 15 Mar 2012, 16:00 → 17:00 Asia/Kolkata

AG-69 (Colaba Campus)

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.