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On trajectories of analytic gradient vector fields on analytic manifolds
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 …