Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


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

  • [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, 10.1112/plms/s3-39.3.428

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58F20, 58F08

Retrieve articles in all journals with MSC: 58F20, 58F08


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0688956-8
Article copyright: © Copyright 1983 American Mathematical Society