Constant slope maps on the extended real line
نویسندگان
چکیده
منابع مشابه
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 the terminology of the Vere-Jones classification of infinite matrices.
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For a function from the unit interval to itself with constant slope and one discontinuity, the itineraries of the point of discontinuity are called the critical itineraries. These critical itineraries play a significant role in the study of β-expansions (with positive or negative β) and fractal transformations. A combinatorial characterization of the critical itineraries of such functions is pr...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2017
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2017.3