7 citations · 27 across the 20 of their papers we have counts for
23 papers
Questions about the dynamics on a natural family of affine cubic surfaces
Julio Rebelo, Roland Roeder
We present several questions about the dynamics of the group of holomorphic automorphisms of the affine cubic surfaces $$S_{A,B,C,D} = \{(x,y,z) \in \mathbb{C}^3 \, : \, x^2 + y^2…
Examples of Harmonic Foliated Currents and Singular Levi-flats on the Projective Plane
Mohamad Alkateeb, Julio Rebelo
We provide examples of foliations on the complex projective plane $\CP^2$ carrying positive foliated harmonic currents whose supports coincide with singular Levi-flats which, in tu…
Global dynamics and perspectives on singularities of holomorphic foliations
Julio C. Rebelo, Helena Reis
In dimensions greater than or equal to 3, the local structure of a singular holomorphic foliation conceals a globally defined foliation on the projective space of dimension one les…
Integrability of vector fields and meromorphic solutions
Julio C. Rebelo, Helena Reis
Let be a foliation defined on a complex projective manifold of dimension and admitting a holomorphic vector field tangent to it along some non-empty Zaris…
Uniformizable singular projective structures on Riemann surface orbifolds
Ahmed Elshafei, Julio C. Rebelo, Helena Reis
This paper is devoted to characterizing complex projective structures defined on Riemann surface orbifolds and giving rise to injective developing maps defined on the monodromy cov…
A remark on first integrals of vector fields
André Belotto da Silva, Martin Klimes, Julio C. Rebelo +1
We provide examples of vector fields on admitting a formal first integral but no holomorphic first integral. These examples are related to a question raised by…
Dynamics of groups of automorphisms of character varieties and Fatou/Julia decomposition for Painlevé 6
Julio Rebelo, Roland Roeder
We study the dynamics of the group of holomorphic automorphisms of the affine cubic surfaces \begin{align*} S_{A,B,C,D} = \{(x,y,z) \in \mathbb{C}^3 \, : \, x^2 + y^2 + z^2 +xyz =…
Palais leaf-space manifolds and surfaces carrying holomorphic flows
Ana Cristina Ferreira, Julio C. Rebelo, Helena Reis
Starting from some remarkable singularities of holomorphic vector fields, we construct (open) complex surfaces over which the singularities in question are realized by complete vec…
Complete commuting vector fields and their singular points in dimension 2
Ana Cristina Ferreira, Julio C. Rebelo, Helena Reis
We classify degenerate singular points of $\C^2$-actions on complex surfaces.
On resolution of 1-dimensional foliations on 3-manifolds
Julio C. Rebelo, Helena Reis
This paper is devoted to the resolution of singularities of holomorphic vector fields and of one-dimensional holomorphic foliations in dimension 3 and it has two main objectives. F…
Global rigidity of conjugations for locally non-discrete subgroups of Diff^w(S^1)
Anas Eskif, Julio C. Rebelo
We prove a global topological rigidity theorem for locally -non-discrete subgroups of the group of real analytic diffeomorphisms of the circle.
2-dimensional Lie algebras and separatrices for vector fields on (C^3,0)
Julio C. Rebelo, Helena Reis
We show that holomorphic vector fields on (C^3,0) have separatrices provided that they are embedded in a rank 2 representation of a two-dimensional Lie algebra. In turn, this resul…
A note on integrability and finite orbits for subgroups of Diff(C^n,0)
Julio C. Rebelo, Helena Reis
In this note we extend to arbitrary dimensions a couple of results due respectively to Mattei-Moussu and to Camara-Scardua in dimension 2. We also provide examples of singular foli…
Discrete orbits, recurrence and solvable subgroups of Diff(C^2,0)
Julio C. Rebelo, Helena Reis
We discuss the local dynamics of a subgroup of Diff(C^2,0) possessing locally discrete orbits as well as the structure of the recurrent set for more general groups. It is proved, i…
Cyclic stabilizers and infinitely many hyperbolic orbits for pseudogroups on (C,0)
Julio C. Rebelo, Helena Reis
Consider a pseudogroup on (C,0) generated by two local diffeomorphisms having analytic conjugacy classes a priori fixed in Diff(C,0). We show that a generic pseudogroup as above is…
On the ergodic theory of certain non-discrete actions and topological orbit equivalences
Julio C. Rebelo
Quasi-invariant measures for non-discrete groups of diffeomorphisms containing a Morse-Smale dynamics are studied. The assumption concerning the presence of a Morse-Smale dynamics…
Discrete orbits and special subgroups of $\Diff$
Julio C. Rebelo, Helena Reis
The local topological dynamics of subgroups of , with special emphasis on , is discussed with a view towards integrabi…
On closed currents invariant by holomorphic foliations, I
Julio C. Rebelo
We consider closed positive currents invariant by a singular holomorphic foliation on an algebraic surface. We show that under some conditions the foliation must leave invariant an…
Generic Pseudogroups on (C,0) and the Topology of Leaves
Jean-François Mattei, Julio C. Rebelo, Helena Reis
We show that generically a pseudogroup generated by holomorphic diffeomorphisms defined about is free in the sense of pseudogroups even if the class of conjugacy…
Uniformizing complex ODEs and applications
Julio C. Rebelo, Helena Reis
We introduce a method to estimate the size of the domain of definition of the solutions of a meromorphic vector field on a neighborhood of its pole divisor. The corresponding techn…
Local Theory of Holomorphic Foliations and Vector Fields
Julio C. Rebelo, Helena Reis
These are slightly informal lecture notes intended for graduate students about the standard local theory of holomorphic foliations and vector fields. Though the material presented…
Fibrations of genus two on complex surfaces
Julio C. Rebelo, Bianca Santoro
We consider fibrations of genus 2 over complex surfaces. The purpose of this paper is primarily to provide a geometric description of the possible structures of the fibration on a…
Complete polynomial vector fields on $\C^2$, Part I
Julio C. Rebelo
In this work, under a mild assumption, we give the classification of the complete polynomial vector fields in two variables up to algebraic automorphisms of $\C^2$. The general pro…