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2024-06-21T10:24:15Z urn:hdl:10324/68177 On restricted analytic gradients on analytic isolated surface singularities Grandjean, Vincent Sanz Sánchez, Fernando 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. 2024-06-21T10:24:15Z 2024-06-21T10:24:15Z 2013 info:eu-repo/semantics/article J. DifferentialEquations255(2013)1684–1708 0022-0396 https://uvadoc.uva.es/handle/10324/68177 10.1016/j.jde.2013.05.020 1684 7 1708 Journal of Differential Equations 255 eng info:eu-repo/semantics/restrictedAccess Elsevier Elsevier