# Semiconjugacy to a map of a constant slope

Date:
30.11.15
Times:
15:30
Place:
UAB - Dept. Matemàtiques (C1/-128)
Speaker:
Lluis Alsedà
University:
UAB

#### 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.