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Natural Invariant


Let rho(x)dx be the fraction of time a typical dynamical map orbit spends in the interval [x,x+dx], and let rho(x) be normalized such that

 int_0^inftyrho(x)dx=1

over the entire interval of the map. Then the fraction the time an map orbit spends in a finite interval [a,b], is given by

 int_a^brho(x)dx.

The natural invariant is also called the invariant density or natural density.


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Cite this as:

Weisstein, Eric W. "Natural Invariant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NaturalInvariant.html

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