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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 $ f$ of a compact interval to itself is linear Markov if it is piecewise linear, and the set of all $ {f^k}(x)$, where $ k \geqslant 0$ and $ x$ 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

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