Stratification of three-dimensional real flows I: Fitting domains
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Title: | Stratification of three-dimensional real flows I: Fitting domains |
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Authors: | Alonso-González, Clementa | Sanz Sánchez, Fernando |
Research Group/s: | Grupo de Álgebra y Geometría (GAG) |
Center, Department or Service: | Universidad de Alicante. Departamento de Matemáticas |
Keywords: | Real vector fields | Singularities | Foliations | Reduction of singularities | Vector fields dynamics |
Issue Date: | 8-Mar-2023 |
Publisher: | Elsevier |
Citation: | Journal of Differential Equations. 2023, 361: 40-96. https://doi.org/10.1016/j.jde.2023.02.029 |
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. The union of the images by π of the local invariant manifolds at those hyperbolic points, denoted by ∧, 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 Fr(Vn) is everywhere tangent to ξexcept around Fr(Vn) ∩ ∧, where transversality is mandatory. |
Sponsor: | The authors were supported by Ministerio de Ciencia e Innovación (MTM2016-77642-C2-1-P and PID2019-105621GB-I00). The second author was also supported by Junta de Castilla y León (VA083G19). |
URI: | http://hdl.handle.net/10045/132799 |
ISSN: | 0022-0396 (Print) | 1090-2732 (Online) |
DOI: | 10.1016/j.jde.2023.02.029 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). |
Peer Review: | si |
Publisher version: | https://doi.org/10.1016/j.jde.2023.02.029 |
Appears in Collections: | INV - GAG - Artículos de Revistas |
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Alonso-Gonzalez_Sanz-Sanchez_2023_JDifferentialEquations.pdf | 2,67 MB | Adobe PDF | Open Preview | |
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