Lyapunov dimension
E695938
The Lyapunov dimension is a fractal dimension used in dynamical systems theory to quantify the effective number of degrees of freedom of a chaotic attractor based on its Lyapunov exponents.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
chaos quantifier
ⓘ
fractal dimension ⓘ invariant of dynamical systems ⓘ |
| appliesTo |
chaotic attractors
ⓘ
dissipative dynamical systems ⓘ |
| basedOn | Lyapunov exponents NERFINISHED ⓘ |
| codomain | non-negative real numbers ⓘ |
| computedFrom | time series via Lyapunov exponent estimation ⓘ |
| dependsOn |
partial sums of ordered Lyapunov exponents
ⓘ
sum of positive Lyapunov exponents ⓘ |
| domain | invariant sets of dynamical systems ⓘ |
| hasAlternativeName |
Kaplan–Yorke Lyapunov dimension
NERFINISHED
ⓘ
Kaplan–Yorke dimension NERFINISHED ⓘ |
| hasMathematicalNature | real-valued function on invariant sets ⓘ |
| hasProperty |
coordinate invariant
ⓘ
invariant under smooth change of variables ⓘ non-integer in typical chaotic systems ⓘ upper bound for Hausdorff dimension in many systems ⓘ |
| introducedBy |
James A. Yorke
NERFINISHED
ⓘ
James L. Kaplan NERFINISHED ⓘ |
| isDefinedFor |
finite-dimensional dynamical systems
ⓘ
flows ⓘ maps ⓘ |
| isFunctionOf | ordered Lyapunov exponents ⓘ |
| namedAfter | Aleksandr Lyapunov NERFINISHED ⓘ |
| quantifies | effective number of degrees of freedom of a chaotic attractor ⓘ |
| relatedTo |
Hausdorff dimension
ⓘ
Kaplan–Yorke conjecture NERFINISHED ⓘ Lyapunov spectrum NERFINISHED ⓘ Pesin theory NERFINISHED ⓘ SRB measures ⓘ correlation dimension ⓘ information dimension ⓘ metric entropy ⓘ |
| usedIn |
biological dynamical systems analysis
ⓘ
chaos theory ⓘ climate dynamics ⓘ dynamical systems theory ⓘ engineering control of chaotic systems ⓘ neural dynamics ⓘ nonlinear dynamics ⓘ secure communications based on chaos ⓘ turbulence modeling ⓘ |
| usedToCharacterize |
complexity of chaotic dynamics
ⓘ
strange attractors ⓘ |
| usedToEstimate |
attractor embedding dimension requirements
ⓘ
fractal dimension of attractors ⓘ |
| yearOfIntroduction | 1979 ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.