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- Uncertainty_exponent abstract "In mathematics, the uncertainty exponent is a method of measuring the fractal dimension of a basin boundary. In a chaotic scattering system, the invariant set of the system is usually not directly accessible because it is non-attracting and typically of measure zero. Therefore, the only way to infer the presence of membersand 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,, in a random direction. If the new trajectory ends upin a different basin from the old one, then it is called epsilon uncertain.If we take a large number of such trajectories,then the fraction of them that are epsilon uncertain is the uncertainty fraction,, and we expect it to scale exponentiallywith Thus the uncertainty exponent, , is defined as follows:The uncertainty exponent can be shown to approximate the box-counting dimensionas follows:where N is the embedding dimension. Please refer to the article on chaotic mixing for an example of numerical computation of the uncertainty dimensioncompared with that of a box-counting dimension.".
- Uncertainty_exponent wikiPageID "27585573".
- Uncertainty_exponent wikiPageRevisionID "446810945".
- Uncertainty_exponent hasPhotoCollection Uncertainty_exponent.
- Uncertainty_exponent subject Category:Chaos_theory.
- Uncertainty_exponent subject Category:Fractals.
- Uncertainty_exponent type Abstraction100002137.
- Uncertainty_exponent type Cognition100023271.
- Uncertainty_exponent type Form105930736.
- Uncertainty_exponent type Fractal105931152.
- Uncertainty_exponent type Fractals.
- Uncertainty_exponent type PsychologicalFeature100023100.
- Uncertainty_exponent type Structure105726345.
- Uncertainty_exponent comment "In mathematics, the uncertainty exponent is a method of measuring the fractal dimension of a basin boundary. In a chaotic scattering system, the invariant set of the system is usually not directly accessible because it is non-attracting and typically of measure zero. Therefore, the only way to infer the presence of membersand to measure the properties of the invariant set is through the basins of attraction.".
- Uncertainty_exponent label "Uncertainty exponent".
- Uncertainty_exponent sameAs m.0c3_3m_.
- Uncertainty_exponent sameAs Q7882494.
- Uncertainty_exponent sameAs Q7882494.
- Uncertainty_exponent sameAs Uncertainty_exponent.
- Uncertainty_exponent wasDerivedFrom Uncertainty_exponent?oldid=446810945.
- Uncertainty_exponent isPrimaryTopicOf Uncertainty_exponent.