15 citations · 27 across the 13 of their papers we have counts for
16 papers
Geometric index theorems for holomorphic foliations and curves
César Camacho, Rudy Rosas
Let be a complex surface endowed with a holomorphic projective connection and let be a compact smooth holomorphic curve. Given two singular holomorphic foliations…
Nondegenerate germs of holomorphic foliations with prescribed holonomy
Javier Ribón, Rudy Rosas
We are interested in characterizing the holonomy maps associated to integral curves of non-degenerate singularities of holomorphic vector fields. Such a description is well-known i…
Transversely product singularities of foliations in projective spaces
Rudy Rosas
We prove that a transversely product component of the singular set of a holomorphic foliation on is necessarily a Kupka component.
A flower theorem in dimension two
Lorena López-Hernanz, Rudy Rosas
We prove a two-dimensional analog of Leau-Fatou flower theorem for non-degenerate reduced tangent to the identity biholomorphisms.
Distributions, first integrals and Legendrian foliations
Maycol Falla Luza, Rudy Rosas
We study germs of holomorphic distributions with "separated variables'. In codimension one, a well know example of this kind of distribution is given by the canonical contact struc…
Chow's theorem for real analytic Levi-flat hypersurfaces
Arturo Fernández-Pérez, Rogério Mol, Rudy Rosas
In this article we provide a version of Chow's theorem for real analytic Levi-flat hypersurfaces in the complex projective space , . More specifically, we…
Foliations on with only one singular point
Percy Fernández, Liliana Puchuri, Rudy Rosas
In this paper we study holomorphic foliations on with only one singular point. If the singularity has algebraic multiplicity one, we prove that the foliation has no…
On singular real analytic Levi-flat foliations
Arturo Fernández-Pérez, Rogério Mol, Rudy Rosas
A singular real analytic foliation of real codimension one on an -dimensional complex manifold is Levi-flat if each of its leaves is foliated by immersed compl…
Foliations on the projective plane with finite group of symmetries
Alan Muniz, Rudy Rosas
Let denote a singular holomorphic foliation on having a finite automorphism group $\mbox{aut}(\mathcal{F})$. Fixed the degree of , we dete…
Characteristic directions of two-dimensional biholomorphisms
Lorena López-Hernanz, Rudy Rosas
We prove that for each characteristic direction of a tangent to the identity diffeomorphism of order in there exist either an analytic curve of fixed poi…
Nodal separators of holomorphic foliations
Rudy Rosas
We study a special kind of local invariant sets of singular holomorphic foliations called nodal separators. We define notions of equisingularity and topological equivalence for nod…
Differentiable equisingularity of holomorphic foliations
Rogério Mol, Rudy Rosas
We prove that a equivalence between germs holomorphic foliations at establishes a bijection between the sets of formal separatrices preserving equi…
On the dynamics of foliations in tangent to Levi-flat hypersurfaces
Arturo Fernández-Pérez, Rogério Mol, Rudy Rosas
Let be a codimension one holomorphic foliation in , , leaving invariant a real-analytic Levi-flat hypersurface with regular part . T…
Invariant sets near singularities of holomorphic foliations
César Camacho, Rudy Rosas
Consider a complex one dimensional foliation on a complex surface near a singularity . If is a closed invariant set containing the singularity , then $\mathcal{…
Bilipschitz invariants for germs of holomorphic foliations
Rudy Rosas
In this paper we study bilipschitz equivalences of germs of holomorphic foliations in . We prove that the algebraic multiplicity of a singularity is invariant by…
Infinitesimal Poincaré-Bendixson Problem in dimension three
C. Alonso-González, F. Cano, R. Rosas
We describe the sets of accumulation of secants for orbits of real analytic vector fields in dimension three having the origin as only ω-limit point. It is a kind of infinitesimal…