| Title:
|
Distributional chaos for flows (English) |
| Author:
|
Zhou, Yunhua |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
475-480 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Schweizer and Smítal introduced the distributional chaos for continuous maps of the interval in B. Schweizer, J. Smítal, Measures of chaos and a spectral decomposition of dynamical systems on the interval. Trans. Amer. Math. Soc. 344 (1994), 737–854. In this paper, we discuss the distributional chaos DC1–DC3 for flows on compact metric spaces. We prove that both the distributional chaos DC1 and DC2 of a flow are equivalent to the time-1 maps and so some properties of DC1 and DC2 for discrete systems also hold for flows. However, we prove that DC2 and DC3 are not invariants of equivalent flows although DC2 is a topological conjugacy invariant in discrete case. (English) |
| Keyword:
|
distributional chaos |
| Keyword:
|
flow |
| Keyword:
|
invariant |
| MSC:
|
37B05 |
| MSC:
|
37B99 |
| MSC:
|
37E25 |
| idZBL:
|
Zbl 06236425 |
| idMR:
|
MR3073972 |
| DOI:
|
10.1007/s10587-013-0031-3 |
| . |
| Date available:
|
2013-07-18T15:02:44Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143326 |
| . |
| Reference:
|
[1] Balibrea, F., Smítal, J., Štefánková, M.: The three versions of distributional chaos.Chaos Solitons Fractals 23 (2005), 1581-1583. Zbl 1069.37013, MR 2101573 |
| Reference:
|
[2] Cao, Y.: Non-zero Lyapunov exponents and uniform hyperbolicity.Nonlinearity 16 (2003), 1473-1479. Zbl 1053.37014, MR 1986306, 10.1088/0951-7715/16/4/316 |
| Reference:
|
[3] Downarowicz, T.: Positive topological entropy implies chaos DC2.Arxiv.org/abs/\allowbreak1110.5201v1. |
| Reference:
|
[4] Schweizer, B., Smítal, J.: Measures of chaos and a spectral decomposition of dynamical systems on the interval.Trans. Am. Math. Soc. 344 (1994), 737-754. Zbl 0812.58062, MR 1227094, 10.1090/S0002-9947-1994-1227094-X |
| Reference:
|
[5] Smítal, J., Štefánková, M.: Distributional chaos for triangular maps.Chaos Solitons Fractals 21 (2004), 1125-1128. Zbl 1060.37037, MR 2047330, 10.1016/j.chaos.2003.12.105 |
| Reference:
|
[6] Sun, W., Young, T., Zhou, Y.: Topological entropies of equivalent smooth flows.Trans. Am. Math. Soc. 361 (2009), 3071-3082. Zbl 1172.37002, MR 2485418, 10.1090/S0002-9947-08-04743-0 |
| . |
