It is proved that a piecewise monotone transformation of the unit interval (with a countable number of pieces) is generically chaotic. The Gauss map arising in connection with the continued fraction expansions of the reals is an example of such a transformation.
@article{bwmeta1.element.bwnjournal-article-apmv63z2p167bwm,
author = {J\'ozef Pi\'orek},
title = {An example of a genuinely discontinuous generically chaotic transformation of the interval},
journal = {Annales Polonici Mathematici},
volume = {63},
year = {1996},
pages = {167-172},
zbl = {0848.54028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv63z2p167bwm}
}
Józef Piórek. An example of a genuinely discontinuous generically chaotic transformation of the interval. Annales Polonici Mathematici, Tome 63 (1996) pp. 167-172. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv63z2p167bwm/
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