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No Semiconjugacy to a Map of Constant Slope

Authors
  • Misiurewicz, Michał
  • Roth, Samuel
Type
Published Article
Publication Date
Mar 11, 2014
Submission Date
Mar 11, 2014
Identifiers
DOI: 10.1017/etds.2014.81
Source
arXiv
License
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External links

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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