Symplectic slices for actions of reductive groups

Let $G$ be a reductive algebraic group over the field $\mathbb C$, $X$ a symplectic smooth affine algebraic variety, $G:X$ a Hamiltonian action, $x$ a point in $X$ with closed orbit. The structure of the variety $X$ in some invariant neighbourhood of the point $x$ is described. The neighbourhood is taken in the complex topology.
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