| Title:
|
Dynamical stability of the typical continuous function (English) |
| Author:
|
Steele, Timothy H. |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
55 |
| Issue:
|
5 |
| Year:
|
2005 |
| Pages:
|
503-514 |
| . |
| Category:
|
math |
| . |
| MSC:
|
26A18 |
| idZBL:
|
Zbl 1150.26002 |
| idMR:
|
MR2200138 |
| . |
| Date available:
|
2009-09-25T14:28:28Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/136922 |
| . |
| Reference:
|
[BCl] BLOCK L.-COPPEL W.: Dynamics in One Dimension.Lecture Notes in Math. 1513, Springer-Verlag, New York, 1991. MR 1176513 |
| Reference:
|
[BBHS] BLOKH A.-BRUCKNER A. M.-HUMKE P. D.-SMÍTAL J.: The space of $\omega$-limit sets of a continuous map of the interval.Trans. Amer. Math. Soc. 348 (1996), 1357-1372. Zbl 0860.54036, MR 1348857 |
| Reference:
|
[B] 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. MR 1433599 |
| Reference:
|
[BBT] BRUCKNER A. M.-BRUCKNER J. B.-THOMSON B. S.: Real Analysis.Prentice-Hall International, Upper Saddle River, NJ, 1997. Zbl 0872.26001 |
| Reference:
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[BC] BRUCKNER A. M.-CEDER J. G.: Chaos in terms of the map $x \mapsto\omega(x,f).Pacific J. Math. 156 (1992), 63-96. MR 1182256 |
| Reference:
|
[BS] BRUCKNER A. M.-SMITAL J.: A characterization of $\omega$-limit sets of maps of the interval with zero topological entropy.Ergodic Theory Dynam. Systems 13 (1993), 7-19. Zbl 0788.58021, MR 1213076 |
| Reference:
|
[FSS] FEDORENKO V.-SARKOVSKII A.-SMITAL J.: Characterizations of weakly chaotic maps of the interval.Proc. Amer. Math. Soc. 110 (1990), 141-148. Zbl 0728.26008, MR 1017846 |
| Reference:
|
[LY] LI T.-YORKE J.: Period three implies chaos.Amer. Math. Monthly 82 (1975), 985-992. Zbl 0351.92021, MR 0385028 |
| Reference:
|
[S] SMITAL J.: Chaotic functions with zero topological entropy.Trans. Amer. Math. Soc. 297 (1986), 269-282. Zbl 0639.54029, MR 0849479 |
| Reference:
|
[STH] SMITAL J.-STEELE T. H.: Stability of dynamical structures under perturbation of the generating function.(Submitted). Zbl 1161.37017 |
| Reference:
|
[TH] STEELE T. H.: Iterative stability in the class of continuous functions.Real Anal. Exchange 24 (1999), 765-780. MR 1704748 |
| Reference:
|
[TH2] STEELE T. H.: Notions of stability for one-dimensional dynamical systems.Int. Math. J. 1 (2002), 543-555. Zbl 1221.37085, MR 1860636 |
| Reference:
|
[TH3] STEELE T. H.: The persistence of $\omega$-limit sets under perturbation of the generating function.Real Anal. Excange 26 (2000), 421-428. Zbl 1056.26019, MR 1844412 |
| . |
