Moscow Mathematical Journal

Volume 24, Issue 1, January–March 2024 pp. 41–61.

On Chaotic Behavior of Ash Attractors

Authors: Elias Rego (1) and Kendry J. Vivas (2)
Author institution:(1) Department of Mathematics, Southern University of Science and Technology, Guangdong Shenzhen, China
(2) Instituto de Matemáticas, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile

Summary:

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 $C^1$ vector field $X$ on a three-dimensional manifold satisfying this kind of hyperbolicity is rescaling expansive and presents sensitiveness respect to initial conditions.

2020 Math. Subj. Class. Primary: 37C10, 37D30; Secondary: 37D45.

Keywords: Flow, attractor, asymptotically sectional-hyperbolic, rescaling expansive.

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