We prove that for continuous interval maps the existence of a non-empty closed invariant subset which is transitive and sensitive to initial conditions is implied by positive topological entropy and implies chaos in the sense of Li-Yorke, and we exhibit examples showing that these three notions are distinct.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-1-6,
author = {Sylvie Ruette},
title = {Transitive sensitive subsystems for interval maps},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {81-104},
zbl = {1094.37020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-1-6}
}
Sylvie Ruette. Transitive sensitive subsystems for interval maps. Studia Mathematica, Tome 166 (2005) pp. 81-104. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-1-6/