Invariant sets near singularities of holomorphic foliationsConsider a complex one-dimensional foliation on a complex surface near a singularity p. If I is a closed invariant set containing the singularity p, then I contains either a separatrix...
Año de publicación: 2015
Flat 3-webs of degree one on the projective planeThe aim of this work is to study global 3-webs with vanishing curvature. We wish to investigate degree 3 foliations for which their dual web is flat. The main ingredient...
Año de publicación: 2014
On codimension one foliations with prescribed cuspidal separatrixIn this paper, we will construct a pre-normal form for germs of codimension one holomorphic foliation having a particular type of separatrix, of cuspidal type. As an application, we will...
Año de publicación: 2014
Vector fields whose linearisation is Hurwitz almost everywhereA real matrix is Hurwitz if its eigenvalues have negative real parts. The following generalisation of the Bidimensional Global Asymptotic Stability Problem (BGAS) is provided. Let X:ℝ2→ℝ2 be a C1...
Año de publicación: 2014
On the limit cycles of a class of Kukles type differential systemsIn this paper we study the limit cycles of two families of differential systems in the plane. These systems are obtained by polynomial perturbations with arbitrary degree on the second...
Año de publicación: 2014
Constructing equivalences with some extensions to the divisor and topological invariance of projective holonomyGiven topologically equivalent germs of holomorphic foliations F and F', under some hypothesis, we construct topological equivalences extending to some regions of the divisor after resolution of singularities. As an...
Año de publicación: 2014
The polar family of webs and foliationsWe define the polar curves and the polar family associated to a projective web and obtain some results about the geometry of the generic element of this family. We also...
Año de publicación: 2014
Infinitesimal Poincaré-Bendixson problem in dimension 3We describe the sets of accumulation of secants for orbits of real analytic vector fields in dimension 3 having the origin as only ω-limit point. It is a kind of...
Año de publicación: 2014
Hubbard ForestsThe theory of Hubbard trees provides an effective classification of nonlinear postcritically finite polynomial maps in ℂ. This note extends the classification to maps from a finite union of copies...
Año de publicación: 2013
Asymptotic stability at infinity for bidimensional Hurwitz vector fieldsLet X:U→ℝ2 be a differentiable vector field. Set Spc(X)={eigenvalues of DX(z) : z∈U}. This X is called Hurwitz if Spc(X)⊂{z∈C : ℜ(z)<0}. Suppose that X is Hurwitz and U⊂ℝ2 is...
Año de publicación: 2013