WIAS Preprint No. 217, (1996)

Shift spaces and attractors in non invertible horse shoes


  • Bothe, Hans Günter

2010 Mathematics Subject Classification

  • 58F12 58F15 58F03


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




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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