English

On Araujo's Theorem for flows

Dynamical Systems 2013-07-23 v1

Abstract

Araujo proved in his thesis \cite{A} that a C1C^1 generic surface diffeomorphism has either infinitely many sinks (i.e. attracting periodic orbits) or finitely many hyperbolic attractors with full Lebesgue measure basin. The goal of this paper is to extend this result to C1C^1 vector fields on compact connected boundaryless manifolds MM of dimension 3 (three-dimensional flows for short). More precisely, we shall prove that a C1C^1 generic three-dimensional flow without singularities has either infinitely many sinks or finitely many hyperbolic attractors with full Lebesgue measure basin.

Keywords

Cite

@article{arxiv.1307.5796,
  title  = {On Araujo's Theorem for flows},
  author = {Alexander Arbieto and Carlos Morales and Bruno Santiago},
  journal= {arXiv preprint arXiv:1307.5796},
  year   = {2013}
}

Comments

20 pages

R2 v1 2026-06-22T00:55:38.584Z