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Transactions of the American Mathematical Society

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Topological semiconjugacy of piecewise monotone maps of the interval

Author: Bill Byers
Journal: Trans. Amer. Math. Soc. 276 (1983), 489-495
MSC: Primary 58F20; Secondary 58F08
MathSciNet review: 688956
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Abstract: This paper establishes a topological semiconjugacy between two piecewise monotone maps of the interval which have the same kneading sequences and do not map one turning point into another, whenever itineraries under the second map are given uniquely by their invariant coordinate. Various examples are given and consequences obtained.

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  • [1] M.V. Jacobson, On smooth mappings of the circle into itself, Math. USSR-Sb. 14 (1971), 161-185.
  • [2] M. V. Jakobson, Topological and metric properties of one-dimensional endomorphisms, Dokl. Akad. Nauk SSSR 243 (1978), no. 4, 866–869 (Russian). MR 514488
  • [3] John Guckenheimer, On the bifurcation of maps of the interval, Invent. Math. 39 (1977), no. 2, 165–178. MR 0438399,
  • [4] John Guckenheimer, Sensitive dependence to initial conditions for one-dimensional maps, Comm. Math. Phys. 70 (1979), no. 2, 133–160. MR 553966
  • [5] M. Milnor and W. Thurston, On iterated maps of the interval. I, preprint, Princeton, 1977. (A complete bibliography may be found in [7].)
  • [6] J. Milnor, A piecewise linear model for kneading, Handwritten Notes, 1976.
  • [7] Pierre Collet and Jean-Pierre Eckmann, Iterated maps on the interval as dynamical systems, Progress in Physics, vol. 1, Birkhäuser, Boston, Mass., 1980. MR 613981
  • [8] P. Fatou, Sur les équations fonctionnelles, Bull. Soc. Math. France 48 (1920), 208–314 (French). MR 1504797
  • [9] G. Julia, Memoire sur l'iteration des fonctions rationelles, J. Math. Pures Appl. 4 (1918), 47-245.
  • [10] Leo Jonker, Periodic orbits and kneading invariants, Proc. London Math. Soc. (3) 39 (1979), no. 3, 428–450. MR 550078,

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Article copyright: © Copyright 1983 American Mathematical Society