Automorphisms of Liouville Structures

By a Liouville structure on a symplectic manifold $(M,\omega )$ we mean a choice of symplectic potential: that is, a choice of one-form $\theta$ on $M$ such that $\mathrm{d}\theta =\omega$. We determine precisely all the automorphisms of a Liouville structure in case $(M,\omega )$ is a symplectic vector space and $\theta$ differs from its canonical symplectic potential by the differential of a homogeneous monomial.