Let
be the fraction of time a typical dynamical map orbit
spends in the interval , and let be normalized such that

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

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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