A chaotic function with zero topological entropy having a non-perfect attractor

Bernd Kirchheim

Mathematica Slovaca (1990)

  • Volume: 40, Issue: 3, page 267-272
  • ISSN: 0232-0525

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Kirchheim, Bernd. "A chaotic function with zero topological entropy having a non-perfect attractor." Mathematica Slovaca 40.3 (1990): 267-272. <http://eudml.org/doc/31808>.

@article{Kirchheim1990,
author = {Kirchheim, Bernd},
journal = {Mathematica Slovaca},
keywords = {chaos; entropy 0; omega-limit; isolated points; periodic points},
language = {eng},
number = {3},
pages = {267-272},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {A chaotic function with zero topological entropy having a non-perfect attractor},
url = {http://eudml.org/doc/31808},
volume = {40},
year = {1990},
}

TY - JOUR
AU - Kirchheim, Bernd
TI - A chaotic function with zero topological entropy having a non-perfect attractor
JO - Mathematica Slovaca
PY - 1990
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 40
IS - 3
SP - 267
EP - 272
LA - eng
KW - chaos; entropy 0; omega-limit; isolated points; periodic points
UR - http://eudml.org/doc/31808
ER -

References

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  1. BLOCK. L., Stability of periodic orbits in the theorem of Sarkovskii, Proc. Amer. Math. Soc. 82. 1981. 333-336. (1981) Zbl0462.54029MR0593484
  2. FALCONER. K. J., Geometry of Fractal Sets, 1st ed. Cambridge University Press 1984. (1984) MR0867284
  3. HSINCHU-XIONG JINGCHENG, A counterexample in dyaynamical systems of [0, 1], Proc. Amer. Math. Soc. 97, 1986. 361-366. (1986) MR0835899
  4. KENŽEGULOV. CH. K., ŠARKOVSKII. A. N., On properties of the set of limit points of an iterated sequence of continuous functions (Russian), Volžsk. Mat. Sb. 3, 1965, 343-348. (1965) MR0199316
  5. ŠARKOVSKII. A. N., Attracting sets containing no cycles (Russian), Ukrain. Mat. Žurn. 20, 1968. 136-142. (1968) MR0225314
  6. ŠARKOVSKII. A. N., On a theorem of G. D. Birkhoff (Russian), Dopov. Akad. Nauk USSR, 1967, No. 5. 429-432. (1967) 
  7. SMÍTAL. J., Chaotic functions with zero topological entropy, Trans. Amer. Math. Soc. 297, 1986. 269-282. (1986) Zbl0639.54029MR0849479
  8. VEREJKINA M. B., ŠARKOVSKII. A. N.: /, Recurrence in one-dimensional dynamical systems, in Approx. and Qualitative Methods of the Theory of Differential & Functional Equations (Russian), Instit. Math. AN USSR. Kiev 1983. pp. 35-46. (1983) MR0753681

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