In Audin's book Morse theory and Floer homology, they claim:
Proposition 6.1.5. Let $H$ be a function on $\mathbb {R^{2n}}$, so that $X_H$ is the Hamiltionian field on $\mathbb {R^{2n}}$. If $|dX_H|_{ L^2 }< 2π$, then the only solutions of period 1 of the Hamiltonian system associated with H are the constant solutions (critical points of H).
I wonder what is the definition of $dX_H$ here.