9 citations · 9 across the 7 of their papers we have counts for
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Analytic normal forms for planar resonant saddle vector fields
Loïc Teyssier
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-sadd…
Rigidity of saddle loops
Daniel Panazzolo, Maja Resman, Loïc Teyssier
A saddle loop is a germ of a holomorphic foliation near a homoclinic saddle connection. We prove that they are classied by their Poincar{é} rst-return map. We also prove that they…
Analytic normal forms and inverse problems for unfoldings of 2-dimensional saddle-nodes with analytic center manifold
C. Rousseau, Loïc Jean Dit Teyssier
We give normal forms for generic k-dimensional parametric families of germs of holomorphic vector fields near unfolding a saddle-no…
Meromorphic infinitesimal affine actions of the plane
Loïc Jean Dit Teyssier
We study complex Lie algebras spanned by pairs \left(Z,Y\right) of germs of a meromorphic vector field of the complex plane satisfying \left[Z,Y\right]=δY for some δ\in\ww C . This…
Analyticity in spaces of convergent power series and applications
Loïc Teyssier
We study the analytic structure of the space of germs of an analytic function at the origin of \ww C^{\times m} , namely the space \germ{\mathbf{z}} where \mathbf{z}=\left(z\_{1},\…
Analytic normal forms for convergent saddle-node vector fields
Reinhard Schäfke, Loïc Jean Dit Teyssier
We give unique analytic "normal forms" for germs of a holomorphic vector field of the complex plane in the neighborhood of an isolated singularity of saddle-node type having a conv…