On the topological entropy of (a,b)-continued fraction transformations
Dynamical Systems
2023-04-26 v1
Abstract
We study the topological entropy of a two-parameter family of maps related to (a,b)-continued fraction algorithms and prove that it is constant on a square within the parameter space (two vertices of this square correspond to well-studied continued fraction algorithms). The proof uses conjugation to maps of constant slope. We also present experimental evidence that the topological entropy is flexible (i.e., takes any value in a range) on the whole parameter space.
Keywords
Cite
@article{arxiv.2210.07389,
title = {On the topological entropy of (a,b)-continued fraction transformations},
author = {Adam Abrams and Svetlana Katok and Ilie Ugarcovici},
journal= {arXiv preprint arXiv:2210.07389},
year = {2023}
}
Comments
14 pages, 10 figures