Typical continuous function without cycles is stable

Katarína Neubrunnová

Mathematica Slovaca (1985)

  • Volume: 35, Issue: 2, page 123-126
  • ISSN: 0232-0525

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Neubrunnová, Katarína. "Typical continuous function without cycles is stable." Mathematica Slovaca 35.2 (1985): 123-126. <http://eudml.org/doc/34202>.

@article{Neubrunnová1985,
author = {Neubrunnová, Katarína},
journal = {Mathematica Slovaca},
keywords = {unstable functions without cycles; stable functions; maps on the compact unit interval; Baire category},
language = {eng},
number = {2},
pages = {123-126},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Typical continuous function without cycles is stable},
url = {http://eudml.org/doc/34202},
volume = {35},
year = {1985},
}

TY - JOUR
AU - Neubrunnová, Katarína
TI - Typical continuous function without cycles is stable
JO - Mathematica Slovaca
PY - 1985
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 35
IS - 2
SP - 123
EP - 126
LA - eng
KW - unstable functions without cycles; stable functions; maps on the compact unit interval; Baire category
UR - http://eudml.org/doc/34202
ER -

References

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  1. BLOCK L., Stability of periodic oгbits in the theorem of Šarkovskii, Pгoc. Ameг. Math. Soc. 81, 1981, 333-336. (1981) MR0593484
  2. COVEN E. M., HEDLUND G. A., Continuous maps of the inteгval whose peгiodic points foгm a closed set, Pгoc. Amer. Math. Soc. 79, 1980, 127-133. (1980) MR0560598
  3. KLOEDEN P., Chaotic difference equations are dense, Bull. Austr. Math. Soc. 15, 1976, 371-379. (1976) Zbl0335.39001MR0432829
  4. LI T. Y., YORKE J. A., Period three implies chaos, Amer. Math. Monthly 82, 1 975, 985-992. Zbl0351.92021MR0385028
  5. MAY R. M., Sirnple mathematical models with very complicated dynamics, Nature 261, 1976, 459-467. (1976) 
  6. SMÍTAL J., SMÍTALOVÁ K., Structural stability of typical nonchaotic difference equations, Journ. Math. Anal. and Appl. 90, 1982, 1-11. (1982) MR0680860
  7. SMÍTAL J., NEUBRUNNOVÁ K., Stability of typical continuous functions with respect to some properties of their iterates, Proc. Amer. Math. Soc. to appear. Zbl0529.54038MR0727258
  8. ШAPKOBCKИЙ A. H., Cocyщecтвoвaниe циклoв нeпpepывнoгo npeoбpaзoвaния npямoй в ceбя, Укpaин. Maт. Жypнaл 16, 1964, 61-71. (1964) 
  9. ШAPKOBCKИЙ A. H., O циклax и cтpyктype нeпpepывнoгo oтoбpaжeния, Укpaин. Maт. Жypнaл 17, 1965, 104-111. (1965) MR0186757

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