  We study the jump of topological entropy for $C^r$ interval or circle maps.
We prove in particular that the topological entropy is continuous at any $f \in
C^r([0; 1])$ with $h_{top}(f) > \frac{\log^+ \|f'\|_\infty}{r}$. To this end we
study the continuity of the entropy of the Buzzi-Hofbauer diagrams associated
to $C^r$ interval maps.
