Tent Map

A piecewise linear, 1-D Map on the interval $[0,1]$ exhibiting Chaotic dynamics and given by

$$x_{n+1} = \mu(1-2\vert x_n-{\textstyle{1\over 2}}\vert).$$

The case $\mu=1$ is equivalent to the Logistic Equation: r=4, so the Natural Invariant in this case is

$$\rho(x)={1\over\pi\sqrt{x(1-x)}}.$$

See also 2x mod 1 Map, Logistic Equation, Logistic Equation: r=4