2013/07/22 by Alexander Arbieto, Arbieto, Alexander, Carlos Morales +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS
paper · pdf · doi:10.48550/arxiv.1307.5796
20 pages
arxiv created 2013/07/22 · arxiv updated 2013/07/23
Araujo proved in his thesis \citeA that a C1 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 C1 vector fields on compact connected boundaryless manifolds M of dimension 3 (three-dimensional flows for short). More precisely, we shall prove that a C1 generic three-dimensional flow without singularities has either infinitely many sinks or finitely many hyperbolic attractors with full Lebesgue measure basin.