Existence of periodic orbits for sectional Anosov flows

2014/07/13 by López, A. M.
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1407.3471

Abstract

We prove that every sectional Anosov flow (or, equivalently, every sectional-hyperbolic attracting set of a flow) on a compact manifold has a periodic orbit. This extends the previous three-dimensional result obtained in [Existence of periodic orbits for singular-hyperbolic sets].

Related

• A note on the density of periodic orbits of Anosov geodesic flow in manifolds of finite volume
• On the essential hyperbolicity of sectional-Anosov flows
• Sectional-Anosov flows in higher dimensions
• Infinitely many closed paths in the graph of Anosov flows
• Hyperbolicity of complements of orbits in Anosov flows