2022/08/02 by Elias Rego, Rego, Elias, Kendry J. Vivas +1 · 1 citation
Mathematics · Physics and Astronomy · #37C10 #37D30 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2208.01553
openalex publication_date 2022/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The asymptotic sectional hyperbolicity is a weak notion of hyperbolicity that extends properly the sectional-hyperbolicity and includes the Rovella attractor as a archetypal example. The main feature of this definition is the existence of arbitrarily large hyperbolic times for points outside the stable manifolds of the singularities. In this paper we will prove that any attractor associated to a C1 vector field X on a three-dimensional manifold satisfying this kind of hyperbolicity is rescaling-expansive and presents sensitiveness respect to initial conditions.