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


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.


  • H. G. Bothe

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