2022/12/08 by Loïc Teyssier, Teyssier, Loïc
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2212.04300
openalex publication_date 2022/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.Abstract. This work is a followup of a similar result obtained for parabolic diffeomorphisms which are tangent to the identity, and solves the long standing problem of finding explicit local analytic models for resonant saddle vector fields.