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

2020/11/30 by Otávio Henrique Perez, Perez, Otavio Henrique, Paulo Ricardo da Silva +1
Engineering · Mathematics · #34A09 #34C08 #Advanced Differential Equations and Dynamical Systems #Control and Dynamics of Mobile Robots #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2012.00085

openalex publication_date 2020/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a theorem of resolution of singularities for real analytic constrained differential systems 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 proof is based on weighted blow-ups and the Newton polygon.

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