We answer affirmatively Coven's question [PC]: Suppose f: I → I is a continuous function of the interval such that every point has at least two preimages. Is it true that the topological entropy of f is greater than or equal to log 2?
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm152-3-4, author = {Jozef Bobok}, title = {The topological entropy versus level sets for interval maps}, journal = {Studia Mathematica}, volume = {151}, year = {2002}, pages = {249-261}, zbl = {1043.37029}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm152-3-4} }
Jozef Bobok. The topological entropy versus level sets for interval maps. Studia Mathematica, Tome 151 (2002) pp. 249-261. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm152-3-4/