WIAS Preprint No. 217, (1996)

Shift spaces and attractors in non invertible horse shoes



Authors

  • Bothe, Hans Günter

2010 Mathematics Subject Classification

  • 58F12 58F15 58F03

Keywords

  • Horse shoes, non invertible maps, shift spaces, attractors

Abstract

As well known, a horse shoe map, i.e. a special injective reimbedding of the unit square I2 in ℝ2 (or more general, of the cube Im in ℝm) as considered first by S. Smale [4], defines a shift dynamics on the maximal invariant subset of I2 (or Im). It is shown that this remains true almost surely for non injective maps provided the contraction of the mapping in the stable direction in sufficiently strong.

Appeared in

  • Fund. Math. 152 (1997) no. 3, pp. 267--289.

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