A two-dimensional piecewise linear map defined by
 |  |  |
(1)
|
 |  |  |
(2)
|
The map is chaotic in the filled region above and stable in the six hexagonal regions. Each point in the interior hexagon defined by the vertices (0, 0), (1, 0), (2, 1),
(2, 2), (1, 2), and (0, 1) has an orbit with period six (except the point (1, 1),
which has period 1). Orbits in the other five hexagonal regions circulate from one
to the other. There is a unique orbit of period five, with all others having period
30. The points having orbits of period five are (
, 3), (
, 
), (3, 
), (5, 3), and (3, 5), indicated in the above figure by the
black line. However, there are infinitely many distinct periodic orbits which have
an arbitrarily long period.
