CR Manifolds Admitting a CR Contraction

Abstract

We classify the germs of C(infinity) CR manifolds that admit a smooth CR contraction. We show that such a CR manifold is embedded into C(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 with its polynomial normal form. Consequently, several results concerning complex and CR geometry are derived.