Generalized horseshoe maps and inverse limits

Sarah Elizabeth Holte

Vol. 156 (1992), No. 2, 297–305

DOI: 10.2140/pjm.1992.156.297

Abstract

The now-classical example due to Smale, the horseshoe map, displays interesting dynamics as well as a topologically complicated attractor. In 1986 Marcy Barge showed that the full attracting sets of horseshoe maps are homeomorphic to inverse limits of the unit interval with a single bonding map. Here we extend Barge’s results to a more general class of maps.

Mathematical Subject Classification 2000

Primary: 58F12

Secondary: 54B99, 54H20

Milestones

Received: 1 February 1991

Revised: 28 May 1991

Published: 1 December 1992