Jumps of entropy for $C^r$ interval maps

David Burguet

Jumps of entropy for $C^r$ interval maps

Dynamical Systems 2015-04-13 v1

Authors: David Burguet

Abstract

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.

Keywords

topological entropy c^r interval maps entropy jumps buzzi-hofbauer diagrams continuity circle maps

Cite

@article{arxiv.1504.02670,
  title  = {Jumps of entropy for $C^r$ interval maps},
  author = {David Burguet},
  journal= {arXiv preprint arXiv:1504.02670},
  year   = {2015}
}

Comments

22 pages

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