No abstract

No abstract

Abstract. We prove the existence of minimal and rigid singular holomorphic foliations by curves on the projective space CP n for every dimension n ≥ 2 and every degree d ≥ 2. Precisely, we construct a foliation F which is induced by a homogeneous vector field of degree d, has a finite singular set and all the regular leaves are dense in the whole of CP n . Moreover, F satisfies many additional properties expected from chaotic dynamics and is rigid in the following sense: if F is conjugate to another holomorphic foliation by a homeomorphism sufficiently close to the identity, then these foliations are also conjugate by a projective transformation. Finally, all these properties are persistent for small perturbations of F. This is done by considering pseudo-groups generated on the unit ball B n ⊂ C n by small perturbations of elements in Diff (C n , 0). Under open conditions on the generators, we prove the existence of many pseudo-flows in their closure (for the C 0 -topology) acting transitively on the ball. Dynamical features as minimality, ergodicity, positive entropy and rigidity may easily be derived from this approach. Finally, some of these pseudo-groups are realized in the transverse dynamics of polynomial vector fields in CP n .

L'accès aux archives de la revue « Annales de l'institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). 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. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/