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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.




© 1996-9 Eric W. Weisstein
1999-05-26