Stratification of three-dimensional real flows II: A generalization of Poincaré's planar sectorial decomposition

2023/06/27 by Alonso-González, Clementa, Sánchez, Fernando Sanz
#34A26 #34A34 #34C08 #34C40 #37C10 #37D05 #37D15 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.15822

Abstract

Let ξ be an analytic vector field in ℝ³ with an isolated singularity at the origin and having only hyperbolic singular points after a reduction of singularities π:M→ℝ³. Assuming certain conditions to be specified throughout the work at hand, we establish a theorem of stratification of the dynamics of ξ that generalizes to dimension three the classical one, coming from Poincaré, about the decomposition of the dynamics of an analytic planar vector field into \em parabolic, \em elliptic or \em hyperbolic invariant sectors.

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