Finiteness of attractors and repellers on sectional hyperbolic sets

2013/09/22 by A. M. López, López, A. M.
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1309.5558

openalex publication_date 2013/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain an upper bound for the number of attractors and repellers that can appear from small perturbations of a sectional hyperbolic set. This extends results from [Sectional-Anosov flows in higher dimensions] and [The explosion of singular-hyperbolic attractors].

Related

• Finiteness of homoclinic classes on sectional hyperbolic sets
• Sectional-Anosov flows in higher dimensions
• Physical measures for asymptotically sectional expanding flows in higher co-dimensions
• On the essential hyperbolicity of sectional-Anosov flows
• The explosion of singular hyperbolic attractors