On families of trajectories of an analytic gradient vector field
Volume 87 / 2005
Annales Polonici Mathematici 87 (2005), 99-109
MSC: Primary 37B35, 58K05; Secondary 14B05, 34C08.
DOI: 10.4064/ap87-0-9
Abstract
For an analytic function $f:\mathbb R^n,0 \rightarrow \Bbb R,0$ having a critical point at the origin, we describe the topological properties of the partition of the family of trajectories of the gradient equation $\dot{x}=\nabla f(x)$ attracted by the origin, given by characteristic exponents and asymptotic critical values.
