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Stratification of three-dimensional real flows I: Fitting domains Alonso González, Clementa Sanz Sánchez, Fernando Matemáticas Geometría Real vector fields Singularities Foliations Campos vectoriales reales Singularidades Foliaciones 12 Matemáticas 1204 Geometría Producción Científica 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. The union of the images by π of the local invariant 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. Ministerio de Ciencia e Innovación (MTM2016-77642-C2-1-P and PID2019- 105621GB-I00) Junta de Castilla y León (VA083G19) 2023-03-13T12:23:04Z 2023-03-13T12:23:04Z 2023 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Journal of Differential Equations, 2023, vol. 361, p. 40-96 0022-0396 https://uvadoc.uva.es/handle/10324/58920 10.1016/j.jde.2023.02.029 40 96 Journal of Differential Equations 361 eng https://www.sciencedirect.com/science/article/pii/S0022039623001055?via%3Dihub Attribution-NonCommercial-NoDerivatives 4.0 Internacional info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ © 2023 The Authors application/pdf Elsevier https://uvadoc.uva.es/bitstream/10324/58920/4/Stratification-of-three-dimensional.pdf.jpg Hispana TEXT http://creativecommons.org/licenses/by-nc-nd/4.0/ UVaDOC. Repositorio Documental de la Universidad de Valladolid https://uvadoc.uva.es/handle/10324/58920