Transition maps at non-resonant hyperbolic singularities are o-minimal

Abstract

We construct a model complete and o-minimal expansion R(2) of the field of real numbers such that, for any planar analytic vector field xi and any isolated, non-resonant hyperbolic singularity p of xi, a transition map for xi at p is definable in R(2). This expansion also defines all convergent generalized power series with natural support and is polynomially bounded.