Trajectories of vector fields asymptotic to formal invariant curves
Producción Científica
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Universidad de Valladolid |
| Repositorio: | UVaDOC. Repositorio Documental de la Universidad de Valladolid |
| OAI Identifier: | oai:dnet:uvadoc______::45eff0ad28f9a9f02f9378e7feff4a89 |
| Acceso en línea: | https://doi.org/10.1017/etds.2026.10291 https://uvadoc.uva.es/handle/10324/84020 |
| Access Level: | acceso abierto |
| Palabra clave: | Curvas algebraicas Algebraic Geometry 12 Matemáticas 1201 Álgebra 1201.01 Geometría Algebraica |
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Trajectories of vector fields asymptotic to formal invariant curvesLe Gal, OlivierSanz Sánchez, FernandoCurvas algebraicasAlgebraic Geometry12 Matemáticas1201 Álgebra1201.01 Geometría AlgebraicaProducción CientíficaWe prove that a formal curve that is invariant by a C ∞ vector field ξ of Rm has a geometrical realization, as soon as the Taylor expansion of ξ is not identically zero along . This means that there is a trajectory γ ⊂ Rm of ξ which is asymptotic to . This result solves a natural question proposed by Bonckaert [Smooth invariant curves of singularities of vector fields in R3. Ann. Inst. Henri Poincaré 3(2) (1986), 111–183] nearly forty years ago. We also construct an invariant C0 manifold S in some open horn around which is composed entirely of trajectories asymptotic to and contains the germ of any such trajectory. If ξ is analytic, we prove that there exists a trajectory γ asymptotic to which is, moreover, non-oscillating with respect to subanalytic sets.Agencia Estatal de Investigación, Ministerio de Ciencia e Innovación - Project PID2019-105621GB-I00 and PID2022-139631NB-I00Cambridge University Press2026info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://doi.org/10.1017/etds.2026.10291https://uvadoc.uva.es/handle/10324/84020reponame:UVaDOC. Repositorio Documental de la Universidad de Valladolidinstname:Universidad de ValladolidIngléshttps://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/trajectories-of-vector-fields-asymptotic-to-formal-invariant-curves/ECB78DA8C29DED89AC37D1334D6BEFF1info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/oai:dnet:uvadoc______::45eff0ad28f9a9f02f9378e7feff4a892026-06-13T12:44:47Z |
| dc.title.none.fl_str_mv |
Trajectories of vector fields asymptotic to formal invariant curves |
| title |
Trajectories of vector fields asymptotic to formal invariant curves |
| spellingShingle |
Trajectories of vector fields asymptotic to formal invariant curves Le Gal, Olivier Curvas algebraicas Algebraic Geometry 12 Matemáticas 1201 Álgebra 1201.01 Geometría Algebraica |
| title_short |
Trajectories of vector fields asymptotic to formal invariant curves |
| title_full |
Trajectories of vector fields asymptotic to formal invariant curves |
| title_fullStr |
Trajectories of vector fields asymptotic to formal invariant curves |
| title_full_unstemmed |
Trajectories of vector fields asymptotic to formal invariant curves |
| title_sort |
Trajectories of vector fields asymptotic to formal invariant curves |
| dc.creator.none.fl_str_mv |
Le Gal, Olivier Sanz Sánchez, Fernando |
| author |
Le Gal, Olivier |
| author_facet |
Le Gal, Olivier Sanz Sánchez, Fernando |
| author_role |
author |
| author2 |
Sanz Sánchez, Fernando |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
Curvas algebraicas Algebraic Geometry 12 Matemáticas 1201 Álgebra 1201.01 Geometría Algebraica |
| topic |
Curvas algebraicas Algebraic Geometry 12 Matemáticas 1201 Álgebra 1201.01 Geometría Algebraica |
| description |
Producción Científica |
| publishDate |
2026 |
| dc.date.none.fl_str_mv |
2026 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
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article |
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publishedVersion |
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https://doi.org/10.1017/etds.2026.10291 https://uvadoc.uva.es/handle/10324/84020 |
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https://doi.org/10.1017/etds.2026.10291 https://uvadoc.uva.es/handle/10324/84020 |
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Inglés |
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Inglés |
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https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/trajectories-of-vector-fields-asymptotic-to-formal-invariant-curves/ECB78DA8C29DED89AC37D1334D6BEFF1 |
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info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/4.0/ |
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openAccess |
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http://creativecommons.org/licenses/by/4.0/ |
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application/pdf |
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Cambridge University Press |
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Cambridge University Press |
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reponame:UVaDOC. Repositorio Documental de la Universidad de Valladolid instname:Universidad de Valladolid |
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Universidad de Valladolid |
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UVaDOC. Repositorio Documental de la Universidad de Valladolid |
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UVaDOC. Repositorio Documental de la Universidad de Valladolid |
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