Traps consist of regions of the piecewise linear
characteristic of slope zero (parallel to the x axis)
or nearly zero. The iteration line is the line
of unit slope linking 
= (0,0) to (1,1). If the
chaotic map has a trap on the iteration line then
eventually the chaotic motion will cease suddenly (figure 2) and the system
will thereafter remain at the fixed point where the trap crosses
the iteration line. If the trap does not intersect the iteration
line (figure 3) then it is likely that the trapped motion will be
periodic (figure 4).
Figure 2: A fixed point trapping.
Figure 4: A periodic trapping.
It is possible that the chaotic motion, usually termed a chaotic transient [5] , can last a very long time. For the map of figure 1, simulations of 100,000 experiments running to trapping gave the statistics shown in figure 5 .
Figure 5: Trapping time distribution.
Although we have not calculated the slope of the exponential fall-off, this in principle should be quite easy; being related to the Liapunov exponent [4] and the structure of the map with its trap.
In the case where the trap lies above or below the iteration line, a little thought shows that the periodicity (number of iterations per cycle) in the trap will vary discontinuously and in a fractal manner as the trap is raised or lowered. If the slope of the trap section is non-zero, then intermittencies occur; the trapped region becomes noisily periodic as in the classic intermittent behaviour described by Pomeau and Manneville [6].
