相关论文: Analytical moduli for unfoldings of saddle-node ve…

We give normal forms for generic k-dimensional parametric families $(Z_\varepsilon)_\varepsilon$ of germs of holomorphic vector fields near $0\in\mathbb{C}^2$ unfolding a saddle-node singularity $Z_0$, under the condition that there exists…

We classify generic unfoldings of germs of antiholomorphic diffeomorphisms with a parabolic point of codimension~$k$ (i.e.~a fixed point of multiplicity $k+1$) under conjugacy. Such generic unfoldings depend real analytically on $k$ real…

When are two germs of analytic systems conjugate or orbitally equivalent under an analytic change of coordinates in the neighborhood of a singular point? A way to answer is to use normal forms. But there are large classes of dynamical…

In this paper we describe the moduli space of germs of generic families of analytic diffeomorphisms which unfold a parabolic fixed point of codimension 1. In [MRR] (and also [R]), it was shown that the Ecalle-Voronin modulus can be unfolded…

We give a complete classification of analytic equivalence of germs of parametric families of systems of complex linear differential equations unfolding a generic resonant singularity of Poincare rank 1 in dimension $n = 2$ whose leading…

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 convergent formal separatrix. We specifically address the…

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…

We classify generic unfoldings of germs of antiholomorphic diffeomorphisms with a parabolic point of codimension 1 (i.e. a double fixed point) under conjugacy. These generic unfolding depend on one real parameter. The classification is done…

In this paper, we study moduli spaces of 2-dimensional complex associative algebras. We give a complete calculation of the cohomology of every element in the moduli space, as well as compute their versal deformations.

In this paper, we identify the moduli space for germs of generic unfoldings of nonresonant linear differential systems with an irregular singularity of Poincar\'e rank $k$ at the origin, under analytic equivalence. The modulus of a given…

We construct the full linearisation functor which takes a graded bundle of degree $k$ (a particular kind of graded manifold) and produces a $k$-fold vector bundle. We fully characterise the image of the full linearisation functor and show…

We give an explicit expression for the (finitely) flat remainder after analytic normal form reduction of a family of planar saddles of diffeomorphisms or vector fields. We distinguish between a rational or irrational ratio of the moduli of…

In this paper we give a geometric description of the foliation of a generic real analytic family unfolding a real analytic vector field with a weak focus at the origin, and show that two such families are orbitally analytically equivalent…

This article is an introduction to some aspects of \'Ecalle's mould calculus, a powerful combinatorial tool which yields surprisingly explicit formulas for the normalising series attached to an analytic germ of singular vector field or of…

Let ${\mathcal C}$ be a fixed equisingularity class of irreducible germs of complex analytic plane curves. We compute a basis of the ${\mathbb C}[[x]]$-module of K\"ahler differentials for generic $\Gamma \in {\mathcal C}$, algorithmically,…

We consider a moduli space of lattice polarized K3 surfaces with the additional information of a frame of the trascendental cohomology with respect to the lattice polarization. This moduli space is proved to be quasi-affine, and the…

In this paper, we study the moduli space of $1|1$-dimensional complex associative algebras. We give a complete calculation of the cohomology of every element in the moduli space, as well as compute their versal deformations.

This work deals with the topological classification of germs of singular foliations on $(\mathbb C^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho-Sad indices and…

This article proposes an initiation to \'Ecalle's mould calculus, a powerful combinatorial tool which yields surprisingly explicit formulas for the normalising series attached to an analytic germ of singular vector field. This is…

The theory of modular deformations is generalized for the category of complex analytic polyhedra which includes germs of complex space as well as any compact complex analytic space. The objective of the theory is a construction of fine…