Examples of $C^r$ interval map with large symbolic extension entropy. .

Abstract

For any integer $r\geq2$ and any real $\epsilon>0$, we construct an explicit example of $\mathcal{C}^r$ interval map $f$ with maximal symbolic extension entropy. Similar examples had been already built by T.Downarowicz and S.Newhouse for diffeomorphisms in higher dimension by using generic arguments on homoclinic tangencies.