The differentiable-invariance of the algebraic multiplicity of a holomorphic vector fieldWe prove that the algebraic multiplicity of a holomorphic vector field at an isolated singularity is invariant by topological equivalences which are differentiable at the singular point.
Año de publicación: 2009
Injectivity of differentiable maps R2→R2 at infinityThe main result given in Theorem 1.1 is a condition for a map X, defined on the complement of a disk D in ℝ2 with values in ℝ2, to be...
Año de publicación: 2006
Asymptotic stability at infinity for differentiable vector fields of the planeLet X:ℝ2\Dσ→ℝ2 be a differentiable (but not necessarily C1) vector field, where σ>0 and Dσ={z∈ℝ2: ∥z∥≤σ}. Denote by R(z) the real part of z∈ℂ. If, for some ϵ>0 and for...
Año de publicación: 2006
On the quasi-ordinary cuspidal foliations in (C3,0)In this paper, we study a class of singularities of codimension 1 holomorphic germs of foliations in (C3,0), namely those ones having only one separatrix, that is a quasi-ordinary surface,...
Año de publicación: 2006
Isolated invariant curves of a foliationWe bound the equisingularity type of the set of isolated separatrices of a holomorphic foliation of in terms of the Milnor number of . This result gives a...
Año de publicación: 2006
An eigenvalue condition for the injectivity and asymptotic stability at infinityLet U → ℝ2 be a differentiable vector field defined on the complement of a compact set. We study the intrinsic relation between the asymptotic behavior of the real eigenvalues of...
Año de publicación: 2005
Automorphisms and non-integrabilityOn this note we prove that a holomorphic foliation of the projective plane with rich, but finite, automorphism group does not have invariant algebraic curves.
Año de publicación: 2005
Global asymptotic stability for differentiable vector fields of R2Let X:R2→R2 be a differentiable map (not necessarily C1), and let Spec(X) denote the set of real or complex eigenvalues of its Jacobian matrix DXp when p varies in R2....
Año de publicación: 2004
On local diffeomorphisms of Rn that are injectiveThere are obtained conditions under which maps from R n to itself are globally injective. In particular there are proved some partial results related to the Weak Markus-Yamabe Conjecture...
Año de publicación: 2004
Transformation groups of holomorphic foliations
We prove that the self-bimeromorphisms group of a foliation of general type on a projective surface is finite. Along the proof we study the structure of arbitrary codimension foliations on...
Año de publicación: 2002
We prove that the self-bimeromorphisms group of a foliation of general type on a projective surface is finite. Along the proof we study the structure of arbitrary codimension foliations on...
Año de publicación: 2002