2026-04-23T20:25:03Zhttps://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/681942024-12-03T14:43:16Zcom_10324_1129com_10324_931com_10324_894col_10324_1193
Champs de vecteurs analytiques et champs de gradients
LION, JEAN-MARIE
MOUSSU, ROBERT
Sanz Sánchez, Fernando
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.
2024-06-22
2024-06-22
2002
info:eu-repo/semantics/article
Ergod. Th. & Dynam. Sys. (2002), 22, 525–534
0143-3857
https://uvadoc.uva.es/handle/10324/68194
10.1017/S0143385702000251
525
02
534
Ergodic Theory and Dynamical Systems
22
1469-4417
fra
info:eu-repo/semantics/restrictedAccess
Cambridge University Press
Cambridge University Press