It is well known that a continuous piecewise monotone interval map with positive topological entropy is semiconjugate to a map of a con-stant 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 contin-uous 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.
|Journal||Discrete and Continuous Dynamical Systems - Series B|
|Publication status||Published - 1 Jan 2015|
- Interval Markov maps
- Measure of maximal entropy
- Piecewise monotonotone maps
- Semiconjugacy to a map of constant slope
- Topological entropy