Tent Map

A piecewise linear, one-dimensional map on the interval exhibiting chaotic dynamics and given by

(1)

The first few iterations of (1) give

			(2)
			(3)
			(4)

where is the initial value, plotted above through five iterations (with increasing iteration number indicated by colors; 1 is red, 2 is yellow, 3 is green, 4 is blue, and 5 is violet) for various values of .

The natural invariant of the tent map is .