Constant Slope Maps and the Vere-Jones Classification

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...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2016-06, Vol.18 (6), p.234
Main Authors: Bobok, Jozef, Bruin, Henk
Format: Article
Language:English
Subjects:
conjugacy
constant slope
interval map
topological entropy
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Summary: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.
ISSN:1099-4300
1099-4300
DOI:10.3390/e18060234