Semiconjugacy to a map of a constant slope
Dynamical Systems
2014-10-08 v1
Abstract
It is well known that a continuous piecewise monotone interval map with positive topological entropy is semiconjugate to a map of a constant slope and the same entropy, and if it is additionally transitive then this semiconjugacy is actually a conjugacy. We generalize this result to piecewise continuous piecewise monotone interval maps, and as a consequence, get it also for piecewise monotone graph maps. We show that assigning to a continuous transitive piecewise monotone map of positive entropy a map of constant slope conjugate to it defines an operator, and show that this operator is not continuous.
Keywords
Cite
@article{arxiv.1410.1718,
title = {Semiconjugacy to a map of a constant slope},
author = {Lluís Alsedà and Michał Misiurewicz},
journal= {arXiv preprint arXiv:1410.1718},
year = {2014}
}