One-dimensional turbulent maps can be characterized via their ω-limit sets [1]. We give a direct proof of this characterization and get stronger results, which allows us to obtain some other results on ω-limit sets, which previously were difficult to prove.
@article{bwmeta1.element.bwnjournal-article-apmv65z3p223bwm,
author = {F. Balibrea and C. La Paz},
title = {Turbulent maps and their $\omega$-limit sets},
journal = {Annales Polonici Mathematici},
volume = {66},
year = {1997},
pages = {223-226},
zbl = {0876.26006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv65z3p223bwm}
}
F. Balibrea; C. La Paz. Turbulent maps and their ω-limit sets. Annales Polonici Mathematici, Tome 66 (1997) pp. 223-226. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv65z3p223bwm/
[000] [1] M. J. Evans, P. D. Humke, C. M. Lee and R. J. O'Malley, Characterizations of turbulent one-dimensional mappings via ω-limit sets, Trans. Amer. Math. Soc. 326 (1991), 261-280.
[001] [2] A. N. Sharkovskiĭ, Coexistence of cycles of a continuous mapping of the line into itself, Ukrain. Mat. Zh. 16 (1964), 61-71 (in Russian). MR 32#4213.
[002] [3] L. S. Block and W. A. Coppel, Dynamics in One Dimension, Lecture Notes in Math. 1513, Springer, Berlin, 1992.