Topological conjugacy and transitivity for a class of piecewise monotone maps of the interval

Authors:
Louis Block and Ethan M. Coven

Journal:
Trans. Amer. Math. Soc. **300** (1987), 297-306

MSC:
Primary 58F08; Secondary 54H20, 58F20

DOI:
https://doi.org/10.1090/S0002-9947-1987-0871677-X

MathSciNet review:
871677

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Abstract: We say that a continuous map of a compact interval to itself is *linear Markov* if it is piecewise linear, and the set of all , where and is an endpoint of a linear piece, is finite. We provide an effective classification, up to topological conjugacy, for linear Markov maps and an effective procedure for determining whether such a map is transitive. We also consider **expanding Markov** maps, partly to motivate the proof of the more complicated linear Markov case.

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DOI:
https://doi.org/10.1090/S0002-9947-1987-0871677-X

Article copyright:
© Copyright 1987
American Mathematical Society