Back to Search
Start Over
Dynamics of the third order Lyness' difference equation.
- Source :
-
Journal of Difference Equations & Applications . Oct2007, Vol. 13 Issue 10, p855-884. 30p. 1 Diagram, 2 Charts, 2 Graphs. - Publication Year :
- 2007
-
Abstract
- This paper studies the iterates of the third order Lyness' recurrence [image omitted] , with positive initial conditions, being a also a positive parameter. It is known that for a = 1 all the sequences generated by this recurrence are 8-periodic. We prove that for each [image omitted] there are infinitely many initial conditions giving rise to periodic sequences which have almost all the even periods and that for a full measure set of initial conditions the sequences generated by the recurrence are dense in either one or two disjoint bounded intervals of . Finally, we show that the set of initial conditions giving rise to periodic sequences of odd period is contained in a co-dimension one algebraic variety (so it has zero measure) and that for an open set of values of a it also contains all the odd numbers, except finitely many of them. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10236198
- Volume :
- 13
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Journal of Difference Equations & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 26655735
- Full Text :
- https://doi.org/10.1080/10236190701264735