
06584243
j
2016c.00867
Griffiths, Jonny
Griffiths, Martin
Lyness cycles and their invariant curves.
Math. Spectr. 48, No. 2, 6772 (2016).
2016
Applied Probability Trust (APT) c/o University of Sheffield, School of Mathematics and Statistics (SoMaS), Sheffield
EN
I75
Lyness cycles
secondorder recurrence relations
invariant curves
Summary: Secondorder recurrence relations are often associated with invariant curves. Although they are not particularly common, some order2 recurrences exhibit periodic behaviour, as their terms repeat, and such recurrences possess invariant curves that are relatively easy to find. In this article we explore some of the properties of these recurrence relations; in particular, we examine the way in which the invariant curves for cycles of different periods can almost coincide, as they degenerate into three straight lines.