RT info:eu-repo/semantics/article
T1 Non oscillating solutions of analytic gradient vector fields
A1 Sanz, Fernando
K1 Vector field - Gradient - Tangent - Oscillation - Blowing-up - Desingularization - Center manifold
AB Let \gamma be an integral solution of an analytic real vector field  defined in a neighbordhood of 0\in R3. Suppose that \gamma has a single limit point at 0. We say that \gamma is non oscillating if, for any analytic surface H, either \gamma is contained in H or \gamma cuts H only finitely many times. In this paper we give a sufficient condition for \gamma to be non oscillating. It is established in terms of the existence of “generalized iterated tangents”, i.e. the existence of a single limit point for any transform property for the solutions of a gradient vector field 𝛻g f of an analytic function f of order 2 at 0, where g is an analytic riemannian metric.
PB Centre Mersenne
SN 0373-0956
YR 1998
FD 1998
LK https://uvadoc.uva.es/handle/10324/68191
UL https://uvadoc.uva.es/handle/10324/68191
LA eng
NO Annales de l’institut Fourier, tome 48, no 4 (1998), p. 1045-1067
DS UVaDOC
RD 22-nov-2024