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

Tomáš Gedeon

Mathematica Slovaca (1991)

  • Volume: 41, Issue: 4, page 379-391
  • ISSN: 0232-0525

How to cite

top

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

top
  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) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.