Geodesic
On a one-dimensional analogue of the Smale horseshoe
Annales Polonici Mathematici, Tome 54 (1991) no. 2, pp. 147-153.

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We construct a transformation T:[0,1] → [0,1] having the following properties: 1) (T,|·|) is completely mixing, where |·| is Lebesgue measure, 2) for every f∈ L¹ with ∫fdx = 1 and φ ∈ C[0,1] we have $∫φ(T^{n}x)f(x)dx → ∫φdμ$, where μ is the cylinder measure on the standard Cantor set, 3) if φ ∈ C[0,1] then $n^{-1}∑_{i=0}^{n-1} φ(T^{i}x) → ∫φdμ$ for Lebesgue-a.e. x.
DOI : 10.4064/ap-54-2-147-153

Ryszard Rudnicki 1

1 
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Ryszard Rudnicki. On a one-dimensional analogue of the Smale horseshoe. Annales Polonici Mathematici, Tome 54 (1991) no. 2, pp. 147-153. doi : 10.4064/ap-54-2-147-153. http://geodesic.mathdoc.fr/articles/10.4064/ap-54-2-147-153/

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