Let $(M,\omega)$ be a symplectic manifold with a hamiltonian effective torus action. Suppose it has an isolated fixed point $p$. Is it true that there exists an invariant neighborhood $U$ of $p$ such that the action on it is linear e.g. $U$ is symplectomorphic to an open ball in $\mathbb C^n$ with standard symplectic form and the torus action is linear? What can be said about local action around fixed submanifolds of dimension greater than $0$?
P.Pushkar told me that it must be true and I can read about it in the journal "Functional analysis and its applications" (Функциональный анализ и его применения) but unfortunately he didn't seem to manage to tell me the author, the name and the year of the publication. Perhaps you can find it.