César Camacho

Minimal sets of foliations on complex projective spaces

© Publications mathématiques de l’I.H.É.S., 1988, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

The topology of holomorphic flows with singularity

© Publications mathématiques de l’I.H.É.S., 1978, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

The topology of integrable differential forms near a singularity

© Publications mathématiques de l’I.H.É.S., 1982, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Holomorphic foliations with Liouvillian first integrals

Intuitively, a Liouvillian function on \mathbb{C} P(n) is one which is obtained from rational functions by a finite process of integrations, exponentiations and algebraic operations. This paper is devoted to the study of foliations determined by polynomial 1-forms which have a Liouvillian first integral. Our main result states that, under some mild restrictions on the singularities of the foliation, such a foliation must be either a linear foliation or an exponent two Bernoulli foliation after some rational pull-back. This proves that the highest level of transcendence for the ordinary differential equations which can be integrated by the use of elementary functions is reached at the Riccati equations.

Fibered neighborhoods of curves in surfaces

The aim of this article is to study fibered neighborhoods of compact holomorphic curves embedded in surfaces. It is shown that when the self-intersection number of the curve is sufficiently negative the fibration is equivalent to the linear one defined in the normal bundle to the curve. The obstructions to equivalence in the general case are described.

The dynamics of the Jouanolou foliation on the complex projective 2-space

We prove that the Jouanolou foliation of degree k 5 admits no nontrivial minimal sets. The proof uses reliable computations based on interval arithmetic.

Morse-Smale R2-Actions on Two-Manifolds

Publisher Summary This chapter discusses Morse–Smale R2-actions on two-manifolds. It also discusses that there exists on any compact 2-manifold a Morse–Smale G-action. The chapter discusses that Morse–Smale G-actions are structurally stable.

Invariant sets near singularities of holomorphic foliations

Consider a complex one-dimensional foliation on a complex surface near a singularity

Residues of Holomorphic Foliations Relative to a General Submanifold

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Holomorphic foliations and Kupka singular sets

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