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math.DS2023
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…
math.DS2014★ 1 cited
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…
math.DS2014
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…