Analytic normal forms for planar resonant saddle vector fields

. We give essentially unique “normal forms” for germs of a holomorphic vector ﬁeld of the complex plane in the neighborhood of an isolated singularity which is a p : q resonant-saddle. Hence each vector ﬁeld of that type is conjugate, by a germ of a biholomorphic map at the singularity, to a preferred element of an explicit family of vector ﬁelds. These model vector ﬁelds are polynomial in the resonant monomial. This work is a followup of a similar result obtained for parabolic di ﬀ eomorphisms which are tangent to the identity, and solves the long standing problem of ﬁnding explicit local analytic models for resonant saddle vector ﬁelds.