A note on generic chaos

Gongfu Liao

Annales Polonici Mathematici (1994)

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

Abstract

top
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.

How to cite

top

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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.