Doi: http://dx.doi.org/10.15446/recolma.v49n1.54162

¹Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil. Email: barragan@im.ufrj.br

A sectional-Anosov flow on a manifold is a C¹ vector field inwardly transverse to the boundary for which the maximal invariant is sectional hyperbolic [10]. We prove that every attractor of every vector field C¹ close to a transitive sectional-Anosov flow with singularities on a compact manifold has a singularity. This extends the three-dimensional result obtained in [9].

Key words: Transitive, Maximal invariant, Sectional-Anosov flow.

Un flujo seccional-Anosov sobre una variedad es un C¹ campo vectorial transversal a la frontera apuntando hacia el interior, para el cual su conjunto maximal invariante es un conjunto seccional hiperbólico [10]. Probamos que todo atractor de todo campo vectorial C¹ próximo a un flujo seccional-Anosov transitivo con singularidades sobre una variedad compacta tiene una singularidad. Este resultado extiende el resultado tres-dimensional obtenido en [9].

Palabras clave: Transitivo, maximal invariante, flujo seccional-Anosov.

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References

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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

Doi: http://dx.doi.org/ @ARTICLE{RCMv49n1a02,
    AUTHOR  = {López, Andrés Mauricio},
    TITLE   = {{Sectional-Anosov Flows in Higher Dimensions}},
    JOURNAL = {Revista Colombiana de Matemáticas},
    YEAR    = {2015},
    volume  = {49},
    number  = {1},
    pages   = {39--55}
}