Instability of equilibria in dimension three

@article{Brunella1998,
abstract = {In this paper we show that if $v$ is an analytic vector field on $\{\Bbb R\}^3$ having an isolated singular point at 0, then there exists a trajectory of $v$ which converges to 0 in the past or in the future. The proof is based on certain results concerning desingularizaton of vector fields in dimension three and on index-type arguments à la Poincaré-Hopf.},
author = {Brunella, Marco},
journal = {Annales de l'institut Fourier},
keywords = {singularities of vector field; invariant manifolds; blow-ups; stability problems; analytic vector fields; isolated singular point; irreducible analytic subvariety; Euler characteristic; unstable point},
language = {eng},
number = {5},
pages = {1345-1357},
publisher = {Association des Annales de l'Institut Fourier},
title = {Instability of equilibria in dimension three},
url = {http://eudml.org/doc/75321},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Brunella, Marco
TI - Instability of equilibria in dimension three
JO - Annales de l'institut Fourier
PY - 1998
PB - Association des Annales de l'Institut Fourier
VL - 48
IS - 5
SP - 1345
EP - 1357
AB - In this paper we show that if $v$ is an analytic vector field on ${\Bbb R}^3$ having an isolated singular point at 0, then there exists a trajectory of $v$ which converges to 0 in the past or in the future. The proof is based on certain results concerning desingularizaton of vector fields in dimension three and on index-type arguments à la Poincaré-Hopf.
LA - eng
KW - singularities of vector field; invariant manifolds; blow-ups; stability problems; analytic vector fields; isolated singular point; irreducible analytic subvariety; Euler characteristic; unstable point
UR - http://eudml.org/doc/75321
ER -