Author:
MISIUREWICZ MICHAŁ,ROTH SAMUEL
Abstract
We study countably piecewise continuous, piecewise monotone interval maps. We establish a necessary and sufficient criterion for the existence of a non-decreasing 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 non-decreasing map. Our examples are continuous and transitive.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Cited by
9 articles.
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1. ON PIECEWISE MONOTONE FUNCTIONS WITH HEIGHT BEING INFINITY;Journal of Applied Analysis & Computation;2021
2. The infimum of Lipschitz constants in the conjugacy class of an interval map;Proceedings of the American Mathematical Society;2018-10-18
3. Constant slope models for finitely generated maps;Discrete & Continuous Dynamical Systems - A;2018
4. Constant slope maps on the extended real line;Ergodic Theory and Dynamical Systems;2017-05-02
5. Counting preimages;Ergodic Theory and Dynamical Systems;2017-01-24