Characterization of chaos for continuous maps of the circle

Milan Kuchta

Commentationes Mathematicae Universitatis Carolinae (1990)

  • Volume: 031, Issue: 2, page 383-390
  • ISSN: 0010-2628

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Kuchta, Milan. "Characterization of chaos for continuous maps of the circle." Commentationes Mathematicae Universitatis Carolinae 031.2 (1990): 383-390. <http://eudml.org/doc/17856>.

@article{Kuchta1990,
author = {Kuchta, Milan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {iteration; continuous maps of the circle; chaos in the sense of Li and Yorke; scrambled set; periodic point},
language = {eng},
number = {2},
pages = {383-390},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Characterization of chaos for continuous maps of the circle},
url = {http://eudml.org/doc/17856},
volume = {031},
year = {1990},
}

TY - JOUR
AU - Kuchta, Milan
TI - Characterization of chaos for continuous maps of the circle
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1990
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 031
IS - 2
SP - 383
EP - 390
LA - eng
KW - iteration; continuous maps of the circle; chaos in the sense of Li and Yorke; scrambled set; periodic point
UR - http://eudml.org/doc/17856
ER -

References

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  1. L. Block, Periods of periodic points of maps of the circle which have a fixed point, Proc. Amer. Math. Soc. 82 (1981), no. 3, pp. 481-486. (1981) Zbl0464.54046MR0612745
  2. L. Block J. Guckenheimer M. Misiurewicz L. S. Young, Periodic points and topological entropy of one-dimensional maps, in book: Global theory of dynamical systems, (Proc. Internal Conf., Northwestern Univ., Evanston, III., 1979, p. 18-34. Lecture Notes in Math. 812, Springer, Berlin 1980 (1979) Zbl0447.58028MR0591173
  3. R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Second Edition, Addison-Wesley, New York 1989. (1989) Zbl0695.58002MR1046376
  4. R. Ito, Rotation sets are closed, Math. Proc. Cambridge Philos. Soc. 89 (1981), no. 1, pp. 107-111. (1981) Zbl0484.58027MR0591976
  5. K. Janková J. Smítal, Characterization of chaos, Bull. Austral. Math. Soc. 34 (1986), no. 2, pp. 283-292. (1986) Zbl0577.54041MR0854575
  6. M. Kuchta J. Smítal, Two point scrambled set implies chaos, in book: European Conference on Iteration Theory, (ECIT 87), World Sci. Publishing Co., Singapore. MR1085314
  7. T. Y. Li J. A. Yorke, Period three implies chaos, Amer. Math. Monthly 82 (1975), no. 10, pp. 985-992. (1975) Zbl0351.92021MR0385028
  8. M. Misiurewicz, Periodic points of maps of degree one of a circle, Ergod. Th. & Dynam. Sys. 2 (1982), no. 2, pp. 221-227. (1982) Zbl0508.58038MR0693977
  9. M. Misiurewicz, Twist sets for maps of the circle, Ergod. Th. & Dynam. Sys. 4 (1984), no. 3, pp. 391-404. (1984) Zbl0573.58019MR0776876
  10. J. Smítal, Chaotic functions with zero topological entropy, Trans. Amer. Math. Soc. 297 (1986), no. 1, pp. 269-282. (1986) MR0849479
  11. A. N. Šarkovskii, On cycles and the structure of a continuous mapping, Ukrain. Mat. Ž. 17 (in Russian) (1965), pp. 104-111. (1965) MR0186757

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