Geodesic
Shift spaces and attractors in noninvertible horseshoes
Fundamenta Mathematicae, Tome 152 (1997) no. 3, pp. 267-289

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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.
DOI : 10.4064/fm-152-3-267-289
Keywords: horseshoes, noninvertible maps, shift spaces, attractors

H. G. Bothe 1

1 
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H. G. Bothe. Shift spaces and attractors in noninvertible horseshoes. Fundamenta Mathematicae, Tome 152 (1997) no. 3, pp. 267-289. doi: 10.4064/fm-152-3-267-289

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