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 , where μ is the cylinder measure on the standard Cantor set, 3) if φ ∈ C[0,1] then for Lebesgue-a.e. x.
1985 Mathematics Subject Classification: Primary 58F13.
@article{bwmeta1.element.bwnjournal-article-apmv54z2p147bwm,
author = {Ryszard Rudnicki},
title = {On a one-dimensional analogue of the Smale horseshoe},
journal = {Annales Polonici Mathematici},
volume = {55},
year = {1991},
pages = {147-153},
zbl = {0731.58047},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv54z2p147bwm}
}
Ryszard Rudnicki. On a one-dimensional analogue of the Smale horseshoe. Annales Polonici Mathematici, Tome 55 (1991) pp. 147-153. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv54z2p147bwm/
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