Jumps of entropy for $C^r$ interval maps
Volume 231 / 2015
Fundamenta Mathematicae 231 (2015), 299-317
MSC: 37A35, 37C05, 37B10, 37B40.
DOI: 10.4064/fm231-3-5
Abstract
We study the jumps 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 $h_{\rm top}(f)>\frac{\log^+\|f'\|_\infty}{r}$. To this end we study the continuity of the entropy of the Buzzi–Hofbauer diagrams associated to $C^r$ interval maps.
