Topological conjugacy and transitivity for a class of piecewise monotone maps of the interval
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- by Louis Block and Ethan M. Coven
- Trans. Amer. Math. Soc. 300 (1987), 297-306
- DOI: https://doi.org/10.1090/S0002-9947-1987-0871677-X
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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.References
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Bibliographic Information
- © Copyright 1987 American Mathematical Society
- 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