The author gives a new detailed proof of a theorem previously proved by Duistermaat in the 1980’s, which claims that the gradient flow of the squared norm of the moment map defines a retract of the appropriate piece of the manifold onto the zero level set of the momentum map. In more technical words: consider the Hamiltonian action of a compact Lie group \(K\) on a symplectic manifold \((M,\sigma)\), endowed with a Riemannian metric compatible with \(\sigma\). Let \(\mu\) be the associated equivariant momentum map, and let \(\phi_t\) be the gradient flow of the norm squared of \(\mu\); that is, the flow of \(-\nabla\mid\mid\mu\mid\mid^2\). Then: 1. For every \(x\in M\), the \(\omega\)-limit set of the trajectory \(\phi_t(x)\) is a single point. 2. For every connected component \(C\) of the set of critical points of \(\mid\mid\mu\mid\mid^2\), the map \(\phi\colon [0,\infty]\times S_C\to C\), \((t,x)\mapsto\phi_t(x)\) (where \(S_C=\{x\in M\;\mid\;\omega-\text{limit}\;\phi_t(x)\subset C\}\)) is a deformation retraction. The proof follows the ideas of [S. Lojasiewicz, “Sur les trajectoires du gradient d’une fonction analytique”, Semin. Geom., Univ. Studi Bologna 1982/1983, 115–117 (1984; Zbl 0606.58045)].