EUDML

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On the Number of Solutions of the Equation ...= ...aj(t)xj, 0...t...1, for which x(0) = x(1).

Alcides Lins Neto — 1980

Inventiones mathematicae

A note on projective Levi flats and minimal sets of algebraic foliations

Alcides Lins Neto — 1999

Annales de l'institut Fourier

In this paper we prove that holomorphic codimension one singular foliations on $ℂ ℙ^{n}, n \geq 3$ have no non trivial minimal sets. We prove also that for $n \geq 3$ , there is no real analytic Levi flat hypersurface in $ℂ ℙ^{n}$ .

Some examples for the Poincaré and Painlevé problems

Alcides Lins Neto — 2002

Annales scientifiques de l'École Normale Supérieure

On Halphen’s Theorem and some generalizations

Alcides Lins Neto — 2006

Annales de l’institut Fourier

Let $M^{n}$ be a germ at $0 \in ℂ^{m}$ of an irreducible analytic set of dimension $n$ , where $n \geq 2$ and $0$ is a singular point of $M$ . We study the question: when does there exist a germ of holomorphic map $φ : (ℂ^{n}, 0) \to (M, 0)$ such that $φ^{- 1} (0) = {0}$ ? We prove essentialy three results. In Theorem 1 we consider the case where $M$ is a quasi-homogeneous complete intersection of $k$ polynomials $F = (F_{1}, ..., F_{k})$ , that is there exists a linear holomorphic vector field $X$ on $ℂ^{m}$ , with eigenvalues $λ_{1}, ..., λ_{m} \in ℚ_{+}$ such that $X (F^{T}) = U \cdot F^{T}$ , where $U$ is a $k \times k$ matrix with entries in $𝒪_{m}$ . We prove that if there exists...

Local structural stability of $C^{2}$ integrable 1-forms

Alcides Lins Neto — 1977

Annales de l'institut Fourier

In this work we consider a class of germs of singularities of integrable 1-forms in $R^{n}$ which are structurally stable in class $C^{r}$ ( $r \geq 2$ if $n = 3$ , $r \geq 4$ if $n \geq 4$ ), whose 1-jet is zero at the singularity. In this class the stability depends essentially on the fact that the perturbations allowed are integrable.