Uncertainty exponent

In mathematics, the uncertainty exponent is a method of measuring the fractal dimension of a basin boundary.

Therefore, the only way to infer the presence of members and to measure the properties of the invariant set is through the basins of attraction.

Note that in a scattering system, basins of attraction are not limit cycles therefore do not constitute members of the invariant set.

Suppose we start with a random trajectory and perturb it by a small amount,

If the new trajectory ends up in a different basin from the old one, then it is called epsilon uncertain.