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oai:uvadoc.uva.es:10324/589202024-12-04T07:25:28Zcom_10324_1129com_10324_931com_10324_894col_10324_1193

Alonso González, Clementa Sanz Sánchez, Fernando Matemáticas 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. 2023-03-13 2023-03-13 2023 info:eu-repo/semantics/article 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 info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ © 2023 The Authors Attribution-NonCommercial-NoDerivatives 4.0 Internacional Elsevier