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

TL;DR

This paper extends the resolution of singularities to 2D real analytic constrained differential systems with corners, using weighted blow-ups and Newton polygons, generalizing classical vector field results.

Contribution

It introduces a resolution theorem for singularities in 2D real analytic constrained systems, broadening classical vector field methods to systems with corners.

Findings

Resolution of singularities achieved for systems with corners

Use of weighted blow-ups and Newton polygon techniques

Generalization of classical vector field results

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.