Normal form of holomorphic dynamical systems

  • Laurent Stolovitch
Part of the NATO Science for Peace and Security Series book series (NAPSB)

This article represents the expanded notes of my lectures at the ASI “Hamiltonian Dynamical Systems and applications”. We shall present various recent results about normal forms of germs of holomorphic vector fields at a fixed point in C n . We shall explain how relevant it is for geometric as well as for dynamical purpose. We shall first give some examples and counter-examples about holomorphic conjugacy. Then, we shall state and prove a main result concerning the holomorphic conjugacy of a commutative family of germs of holomorphic vector fields. For this, we shall explain the role of diophantine condition and the notion of singular complete integrability.

Keywords

Manifold Nash Lost 

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© Springer Science + Business Media B.V 2008

Authors and Affiliations

  • Laurent Stolovitch
    • 1
  1. 1.Laboratoire Emile PicardUniversité Paul SabatierFrance

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