Stable and non-stable non-chaotic maps of the interval

Tomáš Gedeon

Mathematica Slovaca (1991)

  • Volume: 41, Issue: 4, page 379-391
  • ISSN: 0139-9918

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Gedeon, Tomáš. "Stable and non-stable non-chaotic maps of the interval." Mathematica Slovaca 41.4 (1991): 379-391. <http://eudml.org/doc/31913>.

@article{Gedeon1991,
author = {Gedeon, Tomáš},
journal = {Mathematica Slovaca},
keywords = {interval; non-chaotic non-stable map; monotonic function; zero topological entropy},
language = {eng},
number = {4},
pages = {379-391},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Stable and non-stable non-chaotic maps of the interval},
url = {http://eudml.org/doc/31913},
volume = {41},
year = {1991},
}

TY - JOUR
AU - Gedeon, Tomáš
TI - Stable and non-stable non-chaotic maps of the interval
JO - Mathematica Slovaca
PY - 1991
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 41
IS - 4
SP - 379
EP - 391
LA - eng
KW - interval; non-chaotic non-stable map; monotonic function; zero topological entropy
UR - http://eudml.org/doc/31913
ER -

References

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  1. DEN JOY A., Sur les courbes definies les equations différentielles a la surface du tore, J. Math. Pures Appl., IX. Ser. 11 (1932), 333-375. (1932) 
  2. GEDEON T., There are no chaotic mappings with residual scrambled sets, Bull. Austr. Math. Soc. 36 (1987), 411-416. (1987) Zbl0646.26008MR0923822
  3. HARRISON J., Wandering intervals, In: Dynamical Systems and Turbulence. (Warwick 1980), Lecture Notes in Math, vol 898, Springer Berlin, Heidelberg and N. Y., 1981, pp. 154-163. (1980) MR0654888
  4. JANKOVÁ K., SMÍTAL J., A characterization of chaos, Bull. Austr. Math. Soc. 34 (1986), 283-293. (1986) Zbl0577.54041MR0854575
  5. JANKOVÁ K., SMÍTAL J., A Theorem of Sarkovskii characterizing continuous map with zero topological entropy, Math. Slovaca (To appear). MR1016343
  6. PREISS D., SMÍTAL J., A characterization of non-chaotic continuous mappings of the interval stable under small perturbations, Trans. Am. Math. Soc. (To appear). MR0997677
  7. SMÍTAL J., Chaotic functions with zero topological entropy, Trans. Am. Math. Soc. 297 (1986), 269-282. (1986) Zbl0639.54029MR0849479
  8. SMÍTAL J., A chaotic function with scrambled set of positive Lebesque measure, Proc. Am. Math. Soc. 92 (1984), 50-54. (1984) MR0749888
  9. ŠARKOVSKII A. N., The behaviour of a map in a neighbourhood of an attracting set, (Russian), Ukrain. Math. Zh. 18 (1966), 60-83. (1966) MR0212784
  10. ŠARKOVSKII A. N., Attracting sets containing no cycles, (Russian), Ukr. Math. Zh. 20 (1968), 136-142. (1968) MR0225314
  11. ŠARKOVSKII A. N., On cycles and structure of continuous mappings, (Russian), Ukr. Math. Zh. 17 (1965), 104-111. (1965) MR0186757
  12. ŠARKOVSKII A. N., A mapping with zero topological entropy having continuum minimal Cantor sets, (Russian), In: Dynamical Systems and Turbulence. Kiev, 1989, pp. 109-115. (1989) 
  13. van STRIEN S. J., Smooth dynamics on the interval, Preprint (1987). (1987) 

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