Critical itineraries of maps with constant slope and one discontinuity
نویسندگان
چکیده
منابع مشابه
Critical Itineraries of Maps with Constant Slope and One Discontinuity
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...
متن کاملCritical itineraries of maps with constant slope and one discontinuity
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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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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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2014
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004114000486