# A note on generic chaos

Annales Polonici Mathematici (1994)

- Volume: 59, Issue: 2, page 99-105
- ISSN: 0066-2216

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topGongfu Liao. "A note on generic chaos." Annales Polonici Mathematici 59.2 (1994): 99-105. <http://eudml.org/doc/262487>.

@article{GongfuLiao1994,

abstract = {We consider dynamical systems on a separable metric space containing at least two points. It is proved that weak topological mixing implies generic chaos, but the converse is false. As an application, some results of Piórek are simply reproved.},

author = {Gongfu Liao},

journal = {Annales Polonici Mathematici},

keywords = {metric space; dynamical system; topological mixing; generic chaos; topologically mixing dynamical system},

language = {eng},

number = {2},

pages = {99-105},

title = {A note on generic chaos},

url = {http://eudml.org/doc/262487},

volume = {59},

year = {1994},

}

TY - JOUR

AU - Gongfu Liao

TI - A note on generic chaos

JO - Annales Polonici Mathematici

PY - 1994

VL - 59

IS - 2

SP - 99

EP - 105

AB - We consider dynamical systems on a separable metric space containing at least two points. It is proved that weak topological mixing implies generic chaos, but the converse is false. As an application, some results of Piórek are simply reproved.

LA - eng

KW - metric space; dynamical system; topological mixing; generic chaos; topologically mixing dynamical system

UR - http://eudml.org/doc/262487

ER -

## References

top- [1] L. S. Block and W. A. Coppel, Dynamics in One Dimension, Lecture Notes in Math. 1513, Springer, 1992.
- [2] W. A. Coppel, Chaos in one dimension, in: Chaos and Order (Canberra, 1990), World Sci., Singapore, 1991, 14-21.
- [3] K. Janková and J. Smítal, A characterization of chaos, Bull. Austral. Math. Soc. 34 (1986), 283-292. Zbl0577.54041
- [4] T.-Y. Li and J. A. Yorke, Period three implies chaos, Amer. Math. Monthly 82 (1975), 985-992. Zbl0351.92021
- [5] G.-F. Liao, ω-limit sets and chaos for maps of the interval, Northeastern Math. J. 6 (1990), 127-135.
- [6] M. Osikawa and Y. Oono, Chaos in C⁰-endomorphism of interval, Publ. Res. Inst. Math. Sci. 17 (1981), 165-177. Zbl0468.58012
- [7] K. Petersen, Ergodic Theory, Cambridge University Press, 1983.
- [8] J. Piórek, On the generic chaos in dynamical systems, Univ. Iagell. Acta Math. 25 (1985), 293-298. Zbl0587.54061
- [9] J. Piórek, On generic chaos of shifts in function spaces, Ann. Polon. Math. 52 (1990), 139-146. Zbl0719.58005

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