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oai:uvadoc.uva.es:10324/681772025-03-18T11:17:22Zcom_10324_1129com_10324_931com_10324_894col_10324_1193

Grandjean, Vincent Sanz Sánchez, Fernando 2013 Let (X,0) be a real analytic isolated surface singularity at the origin 0 of Rn and let g be a real analytic Riemannian metric at 0∈Rn. Given a real analytic function f0:(Rn,0)→(R,0) singular at 0, weprove that the gradient trajectories for the metric g|X\0 of the restriction (f0|X) escaping from or ending up at 0 do not oscillate. Such a trajectory is thus a sub-pfaffian set. Moreover, in each connected component of X\0 where the restricted gradient does not vanish, there is always a trajectory accumulating at 0 and admitting a formal asymptotic expansion at 0. application/pdf https://uvadoc.uva.es/handle/10324/68177 eng Elsevier On restricted analytic gradients on analytic isolated surface singularities info:eu-repo/semantics/article TEXT UVaDOC. Repositorio Documental de la Universidad de Valladolid Hispana