= Compact gradient-flow trapping criterion
{title2=$\dot V=-\|\nabla V\|^2$}
A smooth <gradient flow> confined to a compact <invariant sublevel set> has finite total integral of $\|\nabla V\|^2$ when $V$ is bounded below. Compactness supplies uniform continuity of that squared norm along the trajectory, so it tends to zero. Every accumulation point is a <critical point>. If the trapped component contains exactly one <critical point>, the trajectory converges to it. This supplies a direct convergence proof in place of an inference solely from an energy-contour picture.
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