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Ulam Map

UlamMap
f(x)=1-2x^2

for x in [-1,1]. Fixed points occur at x=-1, 1/2, and order 2 fixed points at x=(1+/-sqrt(5))/4. The natural invariant of the map is

rho(y)=1/(pisqrt(1-y^2)).

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References

Beck, C. and Schlögl, F. Thermodynamics of Chaotic Systems: An Introduction. Cambridge, England: Cambridge University Press, p. 194, 1995.

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Ulam Map

Cite this as:

Weisstein, Eric W. "Ulam Map." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/UlamMap.html

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