For an analytic function f:ℝⁿ,0 → ℝ,0 having a critical point at the origin, we describe the topological properties of the partition of the family of trajectories of the gradient equation ẋ = ∇f(x) attracted by the origin, given by characteristic exponents and asymptotic critical values.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-9,
author = {Adam Dzedzej and Zbigniew Szafraniec},
title = {On families of trajectories of an analytic gradient vector field},
journal = {Annales Polonici Mathematici},
volume = {85},
year = {2005},
pages = {99-109},
zbl = {1089.37010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-9}
}
Adam Dzedzej; Zbigniew Szafraniec. On families of trajectories of an analytic gradient vector field. Annales Polonici Mathematici, Tome 85 (2005) pp. 99-109. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-9/