## Large topological entropy implies
existence of a maximal entropy measure for interval maps

*Discrete
Contin. Dyn. Syst. Ser. A*, **14** (4), 673-688, 2006.

### Abstract

We give a new type of sufficient condition for the existence of
measures with maximal entropy for an interval map *f*, using
some non-uniform hyperbolicity to compensate for a lack of smoothness
of *f*. More precisely, if the topological entropy of a
*C*^{1} interval map is greater than the sum of the
local entropy and the entropy of the critical points, then there
exists at least one measure with maximal entropy. As a corollary, we
obtain that any *C*^{ r} interval map *f* such that
possesses measures with maximal entropy.

Paper:
[arXiv:1901.01073]
[pdf (published paper)]