2013/08/08 by A. Arbieto, Alexander Arbieto, Anita M. Rojas +5 · 1 citation
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS
paper · pdf · doi:10.48550/arxiv.1308.1734
arxiv created 2013/08/08 · openalex publication_date 2013/08/08 · arxiv updated 2013/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that every C1 generic three-dimensional flow has either infinitely many sinks, or, infinitely many hyperbolic or singular-hyperbolic attractors whose basins form a full Lebesgue measure set. We also prove in the orientable case that the set of accumulation points of the sinks of a C1 generic three-dimensional flow has no dominated splitting with respect to the linear Poincaré flow. As a corollary we obtain that every three-dimensional flow can be C1 approximated by flows with homoclinic tangencies or by singular-Axiom A flows.