A theorem of Šarkovskii characterizing continuous maps of zero topological entropy

Katarína Janková; Jaroslav Smítal

Mathematica Slovaca (1989)

  • Volume: 39, Issue: 3, page 261-265
  • ISSN: 0232-0525

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Janková, Katarína, and Smítal, Jaroslav. "A theorem of Šarkovskii characterizing continuous maps of zero topological entropy." Mathematica Slovaca 39.3 (1989): 261-265. <http://eudml.org/doc/34291>.

@article{Janková1989,
author = {Janková, Katarína, Smítal, Jaroslav},
journal = {Mathematica Slovaca},
keywords = {-limit set; Sharkovskij's theorem; topological entropy; continuous map; periodic point},
language = {eng},
number = {3},
pages = {261-265},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {A theorem of Šarkovskii characterizing continuous maps of zero topological entropy},
url = {http://eudml.org/doc/34291},
volume = {39},
year = {1989},
}

TY - JOUR
AU - Janková, Katarína
AU - Smítal, Jaroslav
TI - A theorem of Šarkovskii characterizing continuous maps of zero topological entropy
JO - Mathematica Slovaca
PY - 1989
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 39
IS - 3
SP - 261
EP - 265
LA - eng
KW - -limit set; Sharkovskij's theorem; topological entropy; continuous map; periodic point
UR - http://eudml.org/doc/34291
ER -

References

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  2. BLOCK L., Homoclinic points of mappings of the interval, Proc Amer. Math. Soc., 72, 1978, 576-580. (1978) Zbl0365.58015MR0509258
  3. JANKOVÁ K., SMÍTAL J., A characterization of chaos, Bull. Austral. Math. Soc., 34, 1986, 283-292. (1986) Zbl0577.54041MR0854575
  4. MISIUREWICZ M., Horseshoes for mappings of the interval, Bull. Acad. Polon. Sci. Sér. Math., 27, 1979, 167-169. (1979) Zbl0459.54031MR0542778
  5. MISIUREWICZ M., SMÍTAL J., Smooth chaotic maps with zero topological entropy, Ergodic Th. & Dynam. Systems, to appear. Zbl0689.58028MR0961740
  6. PREISS D., SMÍTAL J., A characterization of non-chaotic maps of the interval stable under small perturbations, Trans. Amer. Math. Soc., to appear. MR0997677
  7. ŠARKOVSKII A. N., On cycles and the structure of continuous mappings, (Russian.) Ukrain. Mat. Ž., 17, No 3, 1965, 104-111. (1965) MR0186757
  8. ŠARKOVSKII A. N., The behavior of a map in a neighborhood of an attracting set, (Russian.) Ukrain. Mat. Ž., 18, No 2, 1966, 60-83. (1966) MR0212784
  9. ŠARKOVSKII A. N., Ona problem of isomorphism of dynamical systems, (Russian.) Proc. Internat. Conference on Nonlinear Oscillations, Vol. 2, Kiev 1970, 541-545. (1970) 
  10. SMÍTAL J., Chaotic functions with zero topological entropy, Trans. Amer. Math. Soc. 297, 1986, 269-282. (1986) Zbl0639.54029MR0849479

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