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arXiv · 1403.2701

No Semiconjugacy to a Map of Constant Slope

Michał Misiurewicz·Samuel Roth
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Abstract

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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Michał Misiurewicz, Samuel Roth. 2014-03-11. No Semiconjugacy to a Map of Constant Slope. https://doi.org/10.1017/etds.2014.81

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