for . Fixed points occur at , 1/2, and order 2 fixed points at . The natural invariant of the map is
Ulam Map
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References
Beck, C. and Schlögl, F. Thermodynamics of Chaotic Systems: An Introduction. Cambridge, England: Cambridge University Press, p. 194, 1995.Referenced on Wolfram|Alpha
Ulam MapCite this as:
Weisstein, Eric W. "Ulam Map." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/UlamMap.html