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The main goal of this paper is to study robust invariant transitive sets containing singularities for C1 flows on three-dimensional compact boundaryless manifolds:they are partially hyperbolic with volume expanding central direction. Moreover, they are either attractors or repellers. Robust here means that this property cannot be destroyed by small C1-perturbations of the flow.


Le but de ce travail est d'étudier des ensembles invariants robustes ayant des singularités pour des flots C1 sur des variétés tridimensionelles : ce sont des ensembles hyperboliques singuliers. << Robuste >> veut dire ici que cette propriété ne peut être détruite par des perturbations C1 du flot.


This article was originally published in Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, available at

Alternative title: Sur les ensembles transitifs singuliers C1 robustes pour des flots en dimension trois

This work is distributed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).



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