Proceedings of the Japan Academy, Series A, Mathematical Sciences

On unimodal linear transformations and chaos

Shunji Ito, Shigeru Tanaka, and Hitoshi Nakada

Full-text: Open access

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 55, Number 7 (1979), 231-236.

Dates
First available in Project Euclid: 20 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195517205

Digital Object Identifier
doi:10.3792/pjaa.55.231

Mathematical Reviews number (MathSciNet)
MR551718

Zentralblatt MATH identifier
0473.54029

Subjects
Primary: 58F13

Citation

Ito, Shunji; Tanaka, Shigeru; Nakada, Hitoshi. On unimodal linear transformations and chaos. Proc. Japan Acad. Ser. A Math. Sci. 55 (1979), no. 7, 231--236. doi:10.3792/pjaa.55.231. https://projecteuclid.org/euclid.pja/1195517205


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References

  • L. Jonker and D. Rand: A lower bound for the entropy of certain maps of the unit interval (preprint).
  • A. Lasota and J. A. Yorke: On the existence of invariant measures for piecewise monotonic transformations. Trans. Amer. Math. Soc, 186, 481- 488 (1973).
  • T. Y. Li and J. A. Yorke: Period three implies chaos. Amer. Math. Monthly, 82, 985-992 (1975).
  • T. Y. Li and J. A. Yorke: Ergodic transformations from an interval into itself. Trans. Amer. Math. Soc, 235, 183-192 (1978).
  • J. Milnor and W. Thurston: On iterated maps of the interval. I (preprint).
  • P. Stefan: A theorem of Sarkovskii on the existence of periodic orbits of continuous endomorphisms of the line. Comm. Math. Phys., 54, 237-248 (1977).