On trajectories of analytic gradient vector fields on analytic manifolds
Keywords
Singularities, gradient vector fieldsAbstract
Let $f\colon M\to {\mathbb R}$ be an analytic proper function defined in a neighbourhood of a closed ``regular'' (for instance semi-analytic or sub-analytic) set $P\subset f^{-1}(y)$. We show that the set of non-trivial trajectories of the equation $\dot x =\nabla f(x)$ attracted by $P$ has the same Čech-Alexander cohomology groups as $\Omega\cap\{f< y\}$, where $\Omega$ is an appropriately choosen neighbourhood of $P$. There are also given necessary conditions for existence of a trajectory joining two closed ``regular'' subsets of $M$.Downloads
Published
2005-03-01
How to Cite
1.
NOWEL, Aleksandra and SZAFRANIEC, Zbigniew. On trajectories of analytic gradient vector fields on analytic manifolds. Topological Methods in Nonlinear Analysis. Online. 1 March 2005. Vol. 25, no. 1, pp. 167 - 182. [Accessed 26 April 2024].
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