Dynamical stability of the typical continuous function

Timothy H. Steele

Mathematica Slovaca (2005)

  • Volume: 55, Issue: 5, page 503-514
  • ISSN: 0139-9918

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Steele, Timothy H.. "Dynamical stability of the typical continuous function." Mathematica Slovaca 55.5 (2005): 503-514. <http://eudml.org/doc/34614>.

@article{Steele2005,
author = {Steele, Timothy H.},
journal = {Mathematica Slovaca},
keywords = {-limit set; chain recurrence; Baire category},
language = {eng},
number = {5},
pages = {503-514},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Dynamical stability of the typical continuous function},
url = {http://eudml.org/doc/34614},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Steele, Timothy H.
TI - Dynamical stability of the typical continuous function
JO - Mathematica Slovaca
PY - 2005
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 55
IS - 5
SP - 503
EP - 514
LA - eng
KW - -limit set; chain recurrence; Baire category
UR - http://eudml.org/doc/34614
ER -

References

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  1. BLOCK L.-COPPEL W., Dynamics in One Dimension, Lecture Notes in Math. 1513, Springer-Verlag, New York, 1991. (1991) MR1176513
  2. BLOKH A.-BRUCKNER A. M.-HUMKE P. D.-SMÍTAL J., The space of ω -limit sets of a continuous map of the interval, Trans. Amer. Math. Soc. 348 (1996), 1357-1372. (1996) Zbl0860.54036MR1348857
  3. BRUCKNER A. M., Stability in the family of w -limit sets of continuous self maps of the interval, Real Anal. Exchange 22 (1997), 52-57. (1997) MR1433599
  4. BRUCKNER A. M.-BRUCKNER J. B.-THOMSON B. S., Real Analysis, Prentice-Hall International, Upper Saddle River, NJ, 1997. (1997) Zbl0872.26001
  5. BRUCKNER A. M.-CEDER J. G., [unknown], Pacific J. Math. 156 (1992), 63-96. (1992) MR1182256
  6. BRUCKNER A. M.-SMITAL J., A characterization of ω -limit sets of maps of the interval with zero topological entropy, Ergodic Theory Dynam. Systems 13 (1993), 7-19. (1993) Zbl0788.58021MR1213076
  7. FEDORENKO V.-SARKOVSKII A.-SMITAL J., Characterizations of weakly chaotic maps of the interval, Proc. Amer. Math. Soc. 110 (1990), 141-148. (1990) Zbl0728.26008MR1017846
  8. LI T.-YORKE J., Period three implies chaos, Amer. Math. Monthly 82 (1975), 985-992. (1975) Zbl0351.92021MR0385028
  9. SMITAL J., Chaotic functions with zero topological entropy, Trans. Amer. Math. Soc. 297 (1986), 269-282. (1986) Zbl0639.54029MR0849479
  10. SMITAL J.-STEELE T. H., Stability of dynamical structures under perturbation of the generating function, (Submitted). Zbl1161.37017
  11. STEELE T. H., Iterative stability in the class of continuous functions, Real Anal. Exchange 24 (1999), 765-780. (1999) MR1704748
  12. STEELE T. H., Notions of stability for one-dimensional dynamical systems, Int. Math. J. 1 (2002), 543-555. Zbl1221.37085MR1860636
  13. STEELE T. H., The persistence of ω -limit sets under perturbation of the generating function, Real Anal. Excange 26 (2000), 421-428. Zbl1056.26019MR1844412

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