Full attracting sets of annulus maps which are inverse limits of circles
type: Item
instance of: scholarly article
title: Full attracting sets of annulus maps which are inverse limits of circles
zbMATH Open document ID: 0835.58023
DOI: 10.1016/0166-8641(94)00107-E
author: Sarah E. Holte
published in: Topology and its Applications
publication date: 1996-04-25T00:00:00Z
review text: According to \textit{M. Barge} [Pac. J. Math. 121, 29-39 (1986; Zbl 0601.58049)] full attracting sets of maps similar to Smale's horseshoe map are homeomorphic to inverse limits of the unit interval. In this article it is shown that certain annulus maps and maps of the solid torus have full attracting sets which are inverse limits of the unit circle and that these maps restricted to their full attracting sets are topologically conjugate to the shift homeomorphism on the inverse limit space.
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 808348
zbMATH Keywords: maps of solid torus
zbMATH Keywords: annulus maps
zbMATH Keywords: full attracting sets
zbMATH Keywords: inverse limits of the unit circle
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
cites work: Horseshoe maps and inverse limits
cites work: Some applications of an approximation theorem for inverse limits
cites work: Q3993502
cites work: Generalized horseshoe maps and inverse limits
cites work: Inverse limits associated with the forced van der Pol equation
cites work: Embedding -Like Compacta in Manifolds
cites work: Q3361587
full work available at URL: 0166-8641(94)00107-e
OpenAlex ID: W2037255743
description: scientific article; zbMATH DE number 808348