RT info:eu-repo/semantics/article
T1 On restricted analytic gradients on analytic isolated surface singularities
A1 Grandjean, Vincent
A1 Sanz, Fernando
K1 Gradient vector field, Oscillating trajectories, Blowing-up, Reduction of singularities
AB 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.
PB Elsevier
SN 0022-0396
YR 2013
FD 2013
LK https://uvadoc.uva.es/handle/10324/68177
UL https://uvadoc.uva.es/handle/10324/68177
LA eng
NO J. DifferentialEquations255(2013)1684–1708
DS UVaDOC
RD 17-jul-2024