Continued Fraction Map

$\begin{figure}\begin{center}\BoxedEPSF{ContinuedFractionMap.epsf}\end{center}\end{figure}$

$\begin{displaymath} f(x)={1\over x}-\left\lfloor{1\over x}\right\rfloor \end{displaymath}$

for $x\in[0,1]$ , where $\left\lfloor{x}\right\rfloor$ is the Floor Function. The Invariant Density of the map is

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

References

Beck, C. and Schlögl, F. Thermodynamics of Chaotic Systems. Cambridge, England: Cambridge University Press, pp. 194-195, 1995.