Entropy-continuity for interval maps with holes
Dynamical Systems
2016-09-30 v2
Abstract
We study the dependence of the topological entropy of piecewise monotonic maps with holes under perturbations, for example sliding a hole of fixed size at uniform speed or expanding a hole with uniform expansion. We show that under suitable conditions the topological entropy varies locally Hoelder continuously with the local Hoelder exponent depending itself on the value of the topological entropy.
Cite
@article{arxiv.1510.06043,
title = {Entropy-continuity for interval maps with holes},
author = {Oscar F. Bandtlow and Hans Henrik Rugh},
journal= {arXiv preprint arXiv:1510.06043},
year = {2016}
}
Comments
23 pages; section 6 has been considerably simplified following suggestions of a referee; to appear in Ergodic Theory and Dynamical Systems