On C^1 robust singular transitive sets for three-dimensional flows

Authors

Carlos Arnoldo Morales, Université de Bourgogne
Maria José Pacífico, Universidade Federal do Rio de Janeiro
Enrique Ramiro Pujals, CUNY Graduate CenterFollow

Document Type

Article

Publication Date

1-1998

Abstract

Abstract:

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.

Résumé:

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.

Comments

This article was originally published in Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, available at https://doi.org/10.1016/S0764-4442(97)82717-6

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).