Let f: [a,b] → [a,b] be a continuous function of the compact real interval such that (i) for every y ∈ [a,b]; (ii) for some m ∈ ∞,2,3,... there is a countable set L ⊂ [a,b] such that for every y ∈ [a,b]∖L. We show that the topological entropy of f is greater than or equal to log m. This generalizes our previous result for m = 2.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-1-2,
author = {Jozef Bobok},
title = {The topological entropy versus level sets for interval maps (part II)},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {11-27},
zbl = {1058.37025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-1-2}
}
Jozef Bobok. The topological entropy versus level sets for interval maps (part II). Studia Mathematica, Tome 166 (2005) pp. 11-27. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-1-2/