33 citations · 53 across the 17 of their papers we have counts for
13 papers · 1 filter
Complex ODEs, singularity theory and dynamics
Helena Reis
These notes are a slightly enlarged version of my habilitation thesis, where our research interest and main results in the past few years are summarized. Most of the discussion rev…
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…
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…
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…
Topological aspects of completely integrable foliations
Susana Pinheiro, Helena Reis
In this paper it is shown that the existence of two independent holomorphic first integrals for foliations by curves on (C^3,0) is not a topological invariant. More precisely, we p…
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…