Alsedà, LluísMisiurewicz, Michał2016-04-262016-04-262015-12Alsedà, L., & Misiurewicz, M. (2015). Semiconjugacy to a map of a constant slope. Discrete and Continuous Dynamical Systems. Series B, 20(10), 2043-2413.https://hdl.handle.net/1805/9416It 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.enIUPUI Open Access Policypiecewise monotonotone mapssemiconjugacy to a map of constant slopetopological entropyArticle