RT info:eu-repo/semantics/article
T1 Champs de vecteurs analytiques et champs de gradients
A1 LION, JEAN-MARIE
A1 MOUSSU, ROBERT
A1 SANZ, FERNANDO
AB A theorem of Łojasiewicz asserts that any relatively compact solution of areal analytic gradient vector field has finite length. We show here a generalization ofthis result for relatively compact solutions of an analytic vector field X with a smoothinvariant hypersurface, transversally hyperbolic for X, where the restriction of the field isa gradient. This solves some instances of R. Thom’s Gradient Conjecture. Furthermore, ifthe dimension of the ambient space is three, these solutions do not oscillate (in the sensethat they cut an analytic set only finitely many times) ; this can also be applied to somegradient vector fields.
PB Cambridge University Press
SN 0143-3857
YR 2002
FD 2002
LK https://uvadoc.uva.es/handle/10324/68194
UL https://uvadoc.uva.es/handle/10324/68194
LA fra
NO Ergod. Th. & Dynam. Sys. (2002), 22, 525–534
DS UVaDOC
RD 07-ago-2024