Abstract
We show that a map of the interval with topological entropy larger than admits at least one measure of maximal entropy. Moreover the number of measures of maximal entropy is finite. It is a sharp improvement of the 2006 paper of Buzzi and Ruette in the case of maps and solves a conjecture of J. Buzzi stated in his 1995 thesis. The proof uses a variation of a theorem of isomorphism due to J. Buzzi between the interval map and the Markovian shift associated to the Buzzi-Hofbauer diagram.
Publication
Proc. Amer. Math. Soc. 142 (2014), no. 3, 957-968