In this talk, we are interested in the group Aut(X,0) of automorphisms of the germ (X,0) of a complex analytic space. We show that Aut(X,0) contains a contracting automorphism if and only if the singularity (X,0) is quasi-homogeneous. This extends previous results by Favre and Ruggiero for the normal surface case, as well as the recent results by Ornea and Verbitsky for the isolated singularity case. Our proof relies on embeddings and normal forms techniques.
