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Sanz Sánchez, Fernando 2024-06-22T09:36:49Z 2024-06-22T09:36:49Z 1998 Annales de l’institut Fourier, tome 48, no 4 (1998), p. 1045-1067 0373-0956 https://uvadoc.uva.es/handle/10324/68191 10.5802/aif.1648 1045 4 1067 Annales de l’institut Fourier 48 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. Partially supported by DGICYT; PB94-1124 and TMR; ERBFMRXCT96-0040 application/pdf eng Centre Mersenne info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ Attribution-NonCommercial-NoDerivatives 4.0 Internacional Vector field - Gradient - Tangent - Oscillation - Blowing-up - Desingularization - Center manifold Non oscillating solutions of analytic gradient vector fields info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion SI