Shift spaces and attractors in noninvertible horseshoes

Volume 152 / 1997

H. G. Bothe Fundamenta Mathematicae 152 (1997), 267-289 DOI: 10.4064/fm-152-3-267-289

Abstract

As is well known, a horseshoe map, i.e. a special injective reimbedding of the unit square $I^2$ in $ℝ^2$ (or more generally, of the cube $I^m$ in $ℝ^m$) as considered first by S. Smale [5], defines a shift dynamics on the maximal invariant subset of $I^2$ (or $I^m$). It is shown that this remains true almost surely for noninjective maps provided the contraction rate of the mapping in the stable direction is sufficiently strong, and bounds for this rate are given.

Authors

  • H. G. Bothe

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image