Singular strange attractors beyond the boundary of hyperbolic flows
type: Item
instance of: scholarly article
title: Singular strange attractors beyond the boundary of hyperbolic flows
published in: Journal of Differential Equations
publication date: 2022-12-16T00:00:00Z
review text: In this paper the authors prove that the suspension of an expanding attractor of a diffeomorphism of the two-disk can be deformed into a robust singular strange attractor which are not Lorenz-like. An attractor is strange if it has a dense orbit with positive Lyapunov exponent and is Lorenz-like if it is singular-hyperbolic and has a unique singularity, it has a basin diffeomorphic to a solid bi-torus and the vector field is inwardly transverse to the boundary of its basin. Although such definition of Lorez-like attractor is not widely used, it fits well they purpose for this work. They perform the deformation along a one-parameter family of flows (an arc of three-dimensional flows) with only one bifurcating parameter value, which allows one to cross the boundary of hyperbolic vector fields, entering in a region completely filled with vector fields that exhibit singular strange attractors.
reviewed by: Matheus Cheque Bortolan
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 37G35
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 7633388
zbMATH Keywords: flow
zbMATH Keywords: singular strange attractor
zbMATH Keywords: manifold
zbMATH Keywords: Lorenz-like attractor
author: Keonhee Lee
author: C. A. Morales
author: M. J. Pacifico
MaRDI profile type: Publication
full work available at URL: j.jde.2022.11.019
OpenAlex ID: W4310274967
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DOI: 10.1016/J.JDE.2022.11.019
description: scientific article; zbMATH DE number 7633388