Generalization of Weinstein's Morphism

We present a generalization of Weinstein's morphism defined on $\pi_{2k-1} ( \textup{Ham} (M,\omega))$. We use this morphism to show that for $n\geq 2$ the Lie group $SU(2)$ induces an element in $\pi_3(\textup{Ham} (\mathbb{C}P^n,\omega_\textup{FS}))$ of infinite order.