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Open AccessFeature PaperArticle

Constant Slope Maps and the Vere-Jones Classification

by Jozef Bobok 1 and Henk Bruin 2,*
1
Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, 16629 Praha 6, Czech Republic
2
Faculty of Mathematics, University of Vienna, Oskar Morgensternplatz 1, 1090 Wien, Austria
*
Author to whom correspondence should be addressed.
Academic Editor: Tomasz Downarowicz
Entropy 2016, 18(6), 234; https://doi.org/10.3390/e18060234
Received: 22 April 2016 / Revised: 6 June 2016 / Accepted: 16 June 2016 / Published: 22 June 2016
(This article belongs to the Special Issue Entropic Properties of Dynamical Systems)
We study continuous countably-piecewise monotone interval maps and formulate conditions under which these are conjugate to maps of constant slope, particularly when this slope is given by the topological entropy of the map. We confine our investigation to the Markov case and phrase our conditions in the terminology of the Vere-Jones classification of infinite matrices. View Full-Text
Keywords: interval map; topological entropy; conjugacy; constant slope interval map; topological entropy; conjugacy; constant slope
MSC: 37E05; 37B40; 46B25 Show Figures

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MDPI and ACS Style

Bobok, J.; Bruin, H. Constant Slope Maps and the Vere-Jones Classification. Entropy 2016, 18, 234.

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