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Constant slope maps on the extended real line

Published online by Cambridge University Press:  02 May 2017

MICHAŁ MISIUREWICZ  and
SAMUEL ROTH Open the ORCID record for SAMUEL ROTH [Opens in a new window]
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, samuel.roth@math.slu.cz Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warsaw, Poland
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, samuel.roth@math.slu.cz Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warsaw, Poland Mathematical Institute, Silesian University, Na Rybníčku 1, Opava 746 01, Czech Republic
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Abstract

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For a transitive countably piecewise monotone Markov interval map we consider the question of whether there exists a conjugate map of constant slope. The answer varies depending on whether the map is continuous or only piecewise continuous, whether it is mixing or not, what slope we consider and whether the conjugate map is defined on a bounded interval, half-line or the whole real line (with the infinities included).

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 8 , December 2018 , pp. 3145 - 3169
Copyright
© Cambridge University Press, 2017 

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