No Semiconjugacy to a Map of Constant Slope
Dynamical Systems
2021-06-29 v1
Abstract
We study countably piecewise continuous, piecewise monotone interval maps. We establish a necessary and sufficient criterion for the existence of a nondecreasing semiconjugacy to a map of constant slope in terms of the existence of an eigenvector of an operator acting on a space of measures. Then we give sufficient conditions under which this criterion is not satisfied. Finally, we give examples of maps not semiconjugate to a map of constant slope via a nondecreasing map. Our examples are continuous and transitive.
Keywords
Cite
@article{arxiv.1403.2701,
title = {No Semiconjugacy to a Map of Constant Slope},
author = {Michał Misiurewicz and Samuel Roth},
journal= {arXiv preprint arXiv:1403.2701},
year = {2021}
}