| Title:
|
Characterization of chaos for continuous maps of the circle (English) |
| Author:
|
Kuchta, Milan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
31 |
| Issue:
|
2 |
| Year:
|
1990 |
| Pages:
|
383-390 |
| . |
| Category:
|
math |
| . |
| MSC:
|
26A18 |
| MSC:
|
37B99 |
| MSC:
|
37D45 |
| MSC:
|
54H20 |
| MSC:
|
58F13 |
| idZBL:
|
Zbl 0728.26011 |
| idMR:
|
MR1077909 |
| . |
| Date available:
|
2008-06-05T21:44:20Z |
| Last updated:
|
2012-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/106868 |
| . |
| Reference:
|
[1] L. Block: Periods of periodic points of maps of the circle which have a fixed point.Proc. Amer. Math. Soc. 82 (1981), no. 3, pp. 481-486. Zbl 0464.54046, MR 0612745 |
| Reference:
|
[2] L. Block J. Guckenheimer M. Misiurewicz L. S. Young: Periodic points and topological entropy of one-dimensional maps.in book: Global theory of dynamical systems, (Proc. Internal Conf., Northwestern Univ., Evanston, III., 1979, p. 18-34. Lecture Notes in Math. 812, Springer, Berlin 1980 MR 0591173 |
| Reference:
|
[3] R. L. Devaney: An Introduction to Chaotic Dynamical Systems.Second Edition, Addison-Wesley, New York 1989. Zbl 0695.58002, MR 1046376 |
| Reference:
|
[4] R. Ito: Rotation sets are closed.Math. Proc. Cambridge Philos. Soc. 89 (1981), no. 1, pp. 107-111. Zbl 0484.58027, MR 0591976 |
| Reference:
|
[5] K. Janková J. Smítal: Characterization of chaos.Bull. Austral. Math. Soc. 34 (1986), no. 2, pp. 283-292. MR 0854575 |
| Reference:
|
[6] M. Kuchta J. Smítal: Two point scrambled set implies chaos.in book: European Conference on Iteration Theory, (ECIT 87), World Sci. Publishing Co., Singapore. MR 1085314 |
| Reference:
|
[7] T. Y. Li J. A. Yorke: Period three implies chaos.Amer. Math. Monthly 82 (1975), no. 10, pp. 985-992. Zbl 0351.92021, MR 0385028 |
| Reference:
|
[8] M. Misiurewicz: Periodic points of maps of degree one of a circle.Ergod. Th. & Dynam. Sys. 2 (1982), no. 2, pp. 221-227. Zbl 0508.58038, MR 0693977 |
| Reference:
|
[9] M. Misiurewicz: Twist sets for maps of the circle.Ergod. Th. & Dynam. Sys. 4 (1984), no. 3, pp. 391-404. Zbl 0573.58019, MR 0776876 |
| Reference:
|
[10] J. Smítal: Chaotic functions with zero topological entropy.Trans. Amer. Math. Soc. 297 (1986), no. 1, pp. 269-282. MR 0849479 |
| Reference:
|
[11] A. N. Šarkovskii: On cycles and the structure of a continuous mapping.Ukrain. Mat. Ž. 17 (in Russian) (1965), pp. 104-111. MR 0186757 |
| . |
