No semiconjugacy to a map of constant slope

We study countably piecewise continuous, piecewise monotone interval
maps. We establish a necessary and sufficient criterion for the
existence of a nondecreasing 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 nondecreasing map. Our
examples are continuous and transitive.

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