Singular-hyperbolic connecting lemma
type: Item
instance of: scholarly article
title: Singular-hyperbolic connecting lemma
zbMATH Open document ID: 1454.37029
author: Serafin Bautista
author: Yeison Sánchez
author: V. Sales
published in: Qualitative Theory of Dynamical Systems
publication date: 2020-10-12T00:00:00Z
review text: The class of singular-hyperbolic sets is of great interest and contains more objects than that of hyperbolic sets, as for example the Lorenz attractor. Thus, it is important to know what properties of hyperbolic sets can be transported to singular-hyperbolic sets. In this work the authors extend the Sectional-Anosov Connecting Lemma presented in [\textit{S. Bautista} and \textit{C. Morales}, Ergodic Theory Dyn. Syst. 30, No. 2, 339--359 (2010; Zbl 1200.37026)] to singular-hyperbolic sets that contain the unstable manifolds of their hyperbolic subsets (this occurs for Lyapunov stable sets, for example). They do so by removing attraction assumptions (note that singular-hyperbolic sets are not attracting sets, in general). Furthermore, they extend this result to compact manifolds with dimension greater than or equal to three, when the singular-hyperbolic set has codimension one.
reviewed by: Matheus Cheque Bortolan
Mathematics Subject Classification ID: 37D05
Mathematics Subject Classification ID: 37D20
Mathematics Subject Classification ID: 37D10
zbMATH DE Number: 7259121
zbMATH Keywords: Anosov flow
zbMATH Keywords: sectional-Anosov flow
zbMATH Keywords: sensitivity
zbMATH Keywords: singular-hyperbolic sets
zbMATH Keywords: Anosov connecting lemma
MaRDI profile type: Publication
full work available at URL: s12346-020-00412-2
OpenAlex ID: W3047096786
Wikidata QID: Q124837968
cites work: Three-Dimensional Flows
cites work: A sectional-Anosov connecting lemma
cites work: Characterizing omega-limit sets which are closed orbits
cites work: Neighborhoods of hyperbolic sets
cites work: Invariant manifolds
cites work: Q4840149
cites work: A dichotomy for three-dimensional vector fields
DOI: 10.1007/S12346-020-00412-2
description: scientific article; zbMATH DE number 7259121