On a one-dimensional analogue of the Smale horseshoe

@article{RyszardRudnicki1991,
abstract = {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.},
author = {Ryszard Rudnicki},
journal = {Annales Polonici Mathematici},
keywords = {Smale horseshoe; chaos; completely mixing; cylinder measure; invariant measure},
language = {eng},
number = {2},
pages = {147-153},
title = {On a one-dimensional analogue of the Smale horseshoe},
url = {http://eudml.org/doc/262334},
volume = {54},
year = {1991},
}

TY - JOUR
AU - Ryszard Rudnicki
TI - On a one-dimensional analogue of the Smale horseshoe
JO - Annales Polonici Mathematici
PY - 1991
VL - 54
IS - 2
SP - 147
EP - 153
AB - 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.
LA - eng
KW - Smale horseshoe; chaos; completely mixing; cylinder measure; invariant measure
UR - http://eudml.org/doc/262334
ER -