CR manifolds admitting a CR contraction

We classify the germs of ${\mathcal{C}}^{\mathrm{\infty }}$ CR manifolds that admit a smooth CR contraction. We show that such a CR manifold is embedded into ${\text{CC}}^n$ as a real hypersurface defined by a polynomial defining function consisting of monomials whose degrees are completely determined by the extended resonances of the contraction. Furthermore the contraction map extends to a holomorphic contraction that coincides in fact with its polynomial normal form. Consequently, several results concerning Complex and CR geometry are derived.