Displaying similar documents to “Normal forms of invariant vector fields under a finite group action.”

Separatrices for non solvable dynamics on ℂ , 0

Isao Nakai (1994)

Annales de l'institut Fourier

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We define the separatrices for pseudogroups of diffeomorphisms of open neighbourhoods of the origin in the complex plane ℂ and prove their existence for non solvable pseudogroups (Theorem 1). This extends a result by Shcherbakov (in [21]) accurately. Our method also applies to prove the topological rigidity theorem for generic pseudogroups attributed to Shcherbakov (dans [20]).

A Cartan-type result for invariant distances and one-dimensional holomorphic retracts.

Colum Watt (2001)

Publicacions Matemàtiques

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We derive conditions under which a holomorphic mapping of a taut Riemann surface must be an automorphism. This is an analogue involving invariant distances of a result of H. Cartan. Using similar methods we prove an existence result for 1-dimensional holomorphic retracts in a taut complex manifold.

A KAM phenomenon for singular holomorphic vector fields

Laurent Stolovitch (2005)

Publications Mathématiques de l'IHÉS

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Let X be a germ of holomorphic vector field at the origin of and vanishing there. We assume that X is a good perturbation of a “nondegenerate” singular completely integrable system. The latter is associated to a family of linear diagonal vector fields which is assumed to have nontrivial polynomial first integrals (they are generated by the so called “resonant monomials”). We show that X admits many invariant analytic subsets in a neighborhood of the origin. These are...

Some remarks on indices of holomorphic vector fields.

Marco Brunella (1997)

Publicacions Matemàtiques

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One can associate several residue-type indices to a singular point of a two-dimensional holomorphic vector field. Some of these indices depend also on the choice of a separatrix at the singular point. We establish some relations between them, especially when the singular point is a generalized curve and the separatrix is the maximal one. These local results have global consequences, for example concerning the construction of logarithmic forms defining a given holomorphic foliation. ...