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

Abstract

We present a theorem of resolution of singularities for real analytic constrained differential systems $A(x)\dot{x}=F(x)$ 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 proof is based on weighted blow-ups and the Newton polygon.

35 pages, 12 figures