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Monotonic semiconjugacies onto expanding maps of the interval


Author: Bill Byers
Journal: Proc. Amer. Math. Soc. 89 (1983), 371-374
MSC: Primary 58F20; Secondary 54H20
DOI: https://doi.org/10.1090/S0002-9939-1983-0712654-0
MathSciNet review: 712654
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Abstract: A contraction mapping is used to produce a semiconjugacy from a map $ {\tau _1}$ with maximum at $ {c_1}$ to an expanding unimodal map with maximum at $ {c_2}$ under the assumption that there is an interval $ J$ containing $ {c_1}$ such that there is a one-to-one, order-preserving correspondence between the orbit of $ J$ under $ {\tau _1}$ and the orbit of $ {c_2}$ under the expanding map.


References [Enhancements On Off] (What's this?)

  • [1] B. Byers, Topological semiconjugacy of piecewise monotonic maps of the interval, Trans. Amer. Math. Soc. 276 (1983), 489-495. MR 688956 (84i:58097)
  • [2] P. Collet and J. P. Eckmann, Iterated maps on the interval as dynamical systems, Birkhäuser, Boston, Mass., 1980. MR 2541754
  • [3] J. Guckenheimer, Sensitive dependence to initial conditions for one dimensional maps, Comm. Math. Phys. 70 (1979), 133-160. MR 553966 (82c:58037)
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DOI: https://doi.org/10.1090/S0002-9939-1983-0712654-0
Article copyright: © Copyright 1983 American Mathematical Society

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