An 
-cycle is a finite sequence of points
, ..., 
such that, under a map 
,
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
In other words, it is a periodic trajectory which comes back to the same point after 
iterations of the cycle. Every point
of the cycle satisfies 
and is therefore a fixed
point of the mapping 
.
A fixed point of 
is simply a cycle of period 1.
