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No semiconjugacy to a map of constant slope

Published online by Cambridge University Press:  10 November 2014

MICHAŁ MISIUREWICZ  and
SAMUEL ROTH
MICHAŁ MISIUREWICZ
Affiliation:
Department of Mathematical Sciences, Indiana University–Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, IN 46202, USA email mmisiure@math.iupui.edu, sjroth@iupui.edu
SAMUEL ROTH
Affiliation:
Department of Mathematical Sciences, Indiana University–Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, IN 46202, USA email mmisiure@math.iupui.edu, sjroth@iupui.edu
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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 non-decreasing 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 non-decreasing map. Our examples are continuous and transitive.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 3 , May 2016 , pp. 875 - 889
Copyright
© Cambridge University Press, 2014 

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