Cusp Map

$\begin{figure}\begin{center}\BoxedEPSF{CuspMap.epsf scaled 1000}\end{center}\end{figure}$

The function

$\begin{displaymath} f(x)=1-2\vert x\vert^{1/2} \end{displaymath}$

for $x\in[-1,1]$ . The Invariant Density is

$\begin{displaymath} \rho(y)={\textstyle{1\over 2}}(1-y). \end{displaymath}$

References

Beck, C. and Schlögl, F. Thermodynamics of Chaotic Systems. Cambridge, England: Cambridge University Press, p. 195, 1995.