On restricted Analytic Gradients on Analytic Isolated Surface Singularities
Classical Analysis and ODEs
2013-11-14 v1 Algebraic Geometry
Abstract
Let (X,O) be a real analytic isolated surface singularity at the origin o of a real analytic manifold M equipped with a real analytic metric g. Given a real analytic function f:(M,O) --> (R,0) singular at O, we prove that the gradient trajectories for the metric g|(X,O) of the restriction f|X escaping from or ending up at the origin O do not oscillate. Such a trajectory is thus a sub-pfaffian set. Moreover, in each connected component of X\O where the restricted gradient does not vanish, there is always a trajectory accumulating at O and admitting a formal asymptotic expansion at O
Keywords
Cite
@article{arxiv.1105.3888,
title = {On restricted Analytic Gradients on Analytic Isolated Surface Singularities},
author = {Vincent Grandjean and Fernando Sanz},
journal= {arXiv preprint arXiv:1105.3888},
year = {2013}
}