RT info:eu-repo/semantics/article T1 Stratification of three-dimensional real flows I: Fitting domains A1 Alonso González, C. A1 Sanz Sánchez, Fernando K1 Matemáticas K1 Geometría K1 Real vector fields K1 Singularities K1 Foliations K1 Campos vectoriales reales K1 Singularidades K1 Foliaciones K1 12 Matemáticas K1 1204 Geometría AB Let ξ be an analytic vector field in R3 with an isolated singularity at the origin and having only hyperbolicsingular points after a reduction of singularities π : M → R3. The union of the images by π of the localinvariant manifolds at those hyperbolic points, denoted by Λ, is composed of trajectories of ξ accumulating to 0 ∈ R3. Assuming that there are no cycles nor polycycles on the divisor of π , together with a Morse-Smale type property and a non-resonance condition on the eigenvalues at these points, in this paper we prove the existence of a fundamental system {Vn} of neighborhoods well adapted for the description of the local dynamics of ξ : the frontier F r(Vn) is everywhere tangent to ξ except around F r(Vn) ∩ Λ, where transversality is mandatory. PB Elsevier SN 0022-0396 YR 2023 FD 2023 LK https://uvadoc.uva.es/handle/10324/58920 UL https://uvadoc.uva.es/handle/10324/58920 LA eng NO Journal of Differential Equations, 2023, vol. 361, p. 40-96 NO Producción Científica DS UVaDOC RD 11-jul-2024