2022/10/21 by Miguel Delgado Pineda, Arbieto, Alexander, Pineda, Miguel +4 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary 37C10 #Quantum chaos and dynamical systems #Secondary 37C27 #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2210.12038
openalex publication_date 2022/10/21 · openalex created_date 2022/10/30 · openalex updated_date 2026/07/28
In this paper, we make several contributions to the theory of asymptotically sectional-hyperbolic (ASH) flows. First, we prove that every star ASH attractor for a C2 vector field is, in fact, sectional-hyperbolic (SH). Second, we establish that all ASH attractors exhibit the property of entropy flexibility. Additionally, we show that any ASH attractor for three-dimensional vector fields is entropy-expansive and admits periodic orbits. Finally, we provide a lower bound for the growth rate of periodic orbits in an ASH attractor.