Resolution of singularities of 2-dimensional real analytic constrained differential systems

Abstract

We present a constructive and self-contained proof for a theorem of resolution of singularities for real analytic constrained differential systems of the form A(x)x˙=F(x) defined on a 2-manifold with corners having impasse set {x;det⁡A(x)=0}. This result can be seen as a generalization of the classical one for 2-dimensional real analytic vector fields. Our approach does not require general results from algebraic geometry.