Open Access
Original Articles
A Note on Devaney’s Definition of Chaos
Vu Dong TôDONG@UOW.EDU.AUSchool of IT & CSUniversity of WollongongNSW 2522, AustraliaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 29 Sep 2003
- Published Online:
- 03 Jun 2013
- Article type:
- Original Articles
- Language:
- EN
- Article no.:
- 1726037X.2004.10698476
- Pages:
- 23–26
Abstract
Devaney [5] defines a function to be chaotic if it satisfies three conditions: transitivity, having dense set of periodic points and sensitive dependence on initial conditions. Banks et al [2] prove that if the function is continuous then the third condition is implied from the first two and therefore it is redundant. However, if the function is not assumed to be continuous, then it is not known if the third condition is redundant or not.
Keywords
References
- Assaf, D and Gadbois, S.1992 . Definition of Chaos . , 99 ( 865 )
- Banks, J, Brooks, J, Cairns, G, Davis, G and Stacey, P.1992 . On Devaney’s Definition of Chaos . , 99 ( 332–334 )
- Block, LS and Coppel, WA. 1992 . , Vol. 1513 , Springer-Verlag . Lecture Notes in Mathematics
- Crannell, A.1995 . The Role of Transitivity in Devaney’s. Definition of Chaos . , 102 ( 788–793 )
- Devaney, RL.1989 . , 2nd , Addison-Wesley .
- Touhey, P.1997 . Yet Another Definition of Chaos . , 104 ( 411–414 )
- Vellekoop, M and Berglund, R.1994 . On Intervals, Transitivity=Chaos . , 101 ( 353–355 )
Views: 49Downloads: 53Citations: 0




