On the classification of planar constrained differential systems under topological equivalence

2021/05/11 by Otávio Henrique Perez, Perez, Otavio Henrique, Paulo Ricardo da Silva +1
Mathematics · Physics and Astronomy · #34A09 #34C05 #34C08 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2105.04748

openalex publication_date 2021/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper concerns the local study of analytic constrained differential systems (or impasse systems) of the form A(x)x = F(x), x∈ℝ², where F is a vector field and A is a matrix valued function. Using techniques of resolution of singularities with weighted blow ups, we extend well-known results in the literature on topological classification of phase portraits of planar vector fields to the context of such class of systems. We also study and classify phase portraits of constrained systems near singular points of the so called impasse set Δ=\x:det A (x) = 0\.

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