Chaotic difference equations in Rn
- 1 August 1981
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
- Vol. 31 (2) , 217-225
- https://doi.org/10.1017/s1446788700033504
Abstract
Sufficient conditons are given for the chaotic behaviour of difference equations defined in terms of continuous mappings in Rn. These conditions are applicable to both difference equations with snap-back repellors and with saddle points. They are applied here to the twisted-horseshoe difference equation of Guckenheimer, Oster and Ipaktchi.Keywords
This publication has 9 references indexed in Scilit:
- Über die Iteration reeller Funktionen. III.Publicationes Mathematicae Debrecen, 2022
- Snap-back repellers imply chaos in RnJournal of Mathematical Analysis and Applications, 1978
- The dynamics of density dependent population modelsJournal of Mathematical Biology, 1977
- Chaotic behaviour of systems of difference equationsInternational Journal of Systems Science, 1976
- Period Three Implies ChaosThe American Mathematical Monthly, 1975
- Period Three Implies ChaosThe American Mathematical Monthly, 1975
- Differentiable dynamical systemsBulletin of the American Mathematical Society, 1967
- О циклах и структуре непрерынвного отображенияUkrainian Mathematical Journal, 1965