Smooth hypersurfaces with a CR contraction

In this paper we show that a C ∞ real hypersurface in C n + 1 of finite DʹAngelo type admitting a weakly contracting local CR automorphism is CR equivalent to a weighted homogeneous hypersurface. As an application, we show that a bounded pseudoconvex domain in C n + 1 with C ∞ boundary of finite DʹAngelo type with a hyperbolic orbit accumulation point is biholomorphically equivalent to a domain defined by a weighted homogeneous polynomial.