Por favor, use este identificador para citar o enlazar este ítem:https://uvadoc.uva.es/handle/10324/68194
Título
Champs de vecteurs analytiques et champs de gradients
Año del Documento
2002
Editorial
Cambridge University Press
Documento Fuente
Ergod. Th. & Dynam. Sys. (2002), 22, 525–534
Résumé
A theorem of Łojasiewicz asserts that any relatively compact solution of a
real analytic gradient vector field has finite length. We show here a generalization of
this result for relatively compact solutions of an analytic vector field X with a smooth
invariant hypersurface, transversally hyperbolic for X, where the restriction of the field is
a gradient. This solves some instances of R. Thom’s Gradient Conjecture. Furthermore, if
the dimension of the ambient space is three, these solutions do not oscillate (in the sense
that they cut an analytic set only finitely many times) ; this can also be applied to some
gradient vector fields.
ISSN
0143-3857
Revisión por pares
SI
Patrocinador
Travail financ´e par le CNRS et le r´eseau europ´een TMR Sing.Ec.Diff. et Feuilletages
Propietario de los Derechos
Cambridge University Press
Idioma
fra
Tipo de versión
info:eu-repo/semantics/submittedVersion
Derechos
restrictedAccess
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