Linearization of hamiltonian torus action

There is always an equivariant local symplectomorphism with $T_pM$ with its 2-form and linear isotropy action, by the Moser-Weinstein proof. But that constant 2-form then has more possible “equivariant normal forms” than just $\sum dp_i\wedge dq_i$ — see e.g. Dellnitz-Melbourne (1993; pdf).