Transformations T:[0,1] → [0,1] with two monotonic pieces are considered. Under the assumption that T is topologically transitive and , it is proved that the invariant measures concentrated on periodic orbits are dense in the set of all invariant probability measures.
@article{bwmeta1.element.bwnjournal-article-fmv157i2p221bwm,
author = {Franz Hofbauer and Peter Raith},
title = {Density of periodic orbit measures for transformations on the interval with two monotonic pieces},
journal = {Fundamenta Mathematicae},
volume = {158},
year = {1998},
pages = {221-234},
zbl = {0915.58026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv157i2p221bwm}
}
Hofbauer, Franz; Raith, Peter. Density of periodic orbit measures for transformations on the interval with two monotonic pieces. Fundamenta Mathematicae, Tome 158 (1998) pp. 221-234. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv157i2p221bwm/
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