Benettin algorithm
E695942
The Benettin algorithm is a numerical method used in dynamical systems theory to estimate Lyapunov exponents, which quantify the rate of separation of nearby trajectories and indicate chaos.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Benettin algorithm canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T7833172 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Benettin algorithm Context triple: [Lyapunov exponents, computedBy, Benettin algorithm]
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A.
Berlekamp–Massey algorithm
The Berlekamp–Massey algorithm is a key algorithm in coding theory and cryptography used to efficiently determine the shortest linear feedback shift register that generates a given binary sequence.
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B.
Cantor–Zassenhaus algorithm
The Cantor–Zassenhaus algorithm is a probabilistic method used to factor polynomials over finite fields efficiently, widely employed in computational algebra and cryptography.
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C.
Cooley–Tukey Fast Fourier Transform algorithm
The Cooley–Tukey Fast Fourier Transform algorithm is a widely used, efficient method for computing the discrete Fourier transform that revolutionized digital signal processing and numerical analysis.
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D.
Marzullo's algorithm
Marzullo's algorithm is a method for selecting the most likely correct time interval from multiple, possibly conflicting time sources, commonly used in clock synchronization systems.
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E.
Blum–Blum–Shub pseudorandom number generator
The Blum–Blum–Shub pseudorandom number generator is a cryptographically secure generator based on the hardness of factoring large composite numbers, widely studied in theoretical computer science and cryptography.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Benettin algorithm Target entity description: The Benettin algorithm is a numerical method used in dynamical systems theory to estimate Lyapunov exponents, which quantify the rate of separation of nearby trajectories and indicate chaos.
-
A.
Berlekamp–Massey algorithm
The Berlekamp–Massey algorithm is a key algorithm in coding theory and cryptography used to efficiently determine the shortest linear feedback shift register that generates a given binary sequence.
-
B.
Cantor–Zassenhaus algorithm
The Cantor–Zassenhaus algorithm is a probabilistic method used to factor polynomials over finite fields efficiently, widely employed in computational algebra and cryptography.
-
C.
Cooley–Tukey Fast Fourier Transform algorithm
The Cooley–Tukey Fast Fourier Transform algorithm is a widely used, efficient method for computing the discrete Fourier transform that revolutionized digital signal processing and numerical analysis.
-
D.
Marzullo's algorithm
Marzullo's algorithm is a method for selecting the most likely correct time interval from multiple, possibly conflicting time sources, commonly used in clock synchronization systems.
-
E.
Blum–Blum–Shub pseudorandom number generator
The Blum–Blum–Shub pseudorandom number generator is a cryptographically secure generator based on the hardness of factoring large composite numbers, widely studied in theoretical computer science and cryptography.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
algorithm in dynamical systems theory
ⓘ
method for computing Lyapunov exponents ⓘ numerical algorithm ⓘ |
| alternativeTo |
QR-decomposition Lyapunov methods
ⓘ
Wolf algorithm for Lyapunov exponents ⓘ |
| appliesTo |
continuous-time dynamical systems
ⓘ
discrete-time dynamical systems ⓘ |
| assumes |
existence of Lyapunov exponents
ⓘ
smoothness of the dynamical system ⓘ |
| basedOn |
evolution of tangent vectors along trajectories
ⓘ
linearization of the flow around a trajectory ⓘ |
| canCompute | spectrum of Lyapunov exponents ⓘ |
| category | computational method in chaos analysis ⓘ |
| computes | maximal Lyapunov exponent ⓘ |
| developedBy | Giancarlo Benettin ⓘ |
| field |
chaos theory
ⓘ
dynamical systems ⓘ nonlinear dynamics ⓘ |
| hasKeyStep |
accumulation of growth rates of perturbation norms
ⓘ
integration of the reference trajectory ⓘ periodic renormalization of perturbation vectors ⓘ simultaneous integration of perturbation vectors ⓘ |
| hasProperty |
iterative
ⓘ
numerically intensive ⓘ sensitive to integration accuracy ⓘ |
| involves |
logarithmic averaging of perturbation growth
ⓘ
long-time integration to reach asymptotic regime ⓘ |
| output | numerical estimates of Lyapunov exponents ⓘ |
| relatedTo |
Gram–Schmidt orthonormalization
ⓘ
linked to:
Schmidt orthogonalization
Lyapunov characteristic exponents ⓘ
linked to:
Lyapunov exponents
Oseledec multiplicative ergodic theorem ⓘ
linked to:
Oseledets theorem
QR-based Lyapunov exponent algorithms ⓘ |
| requires |
Gram–Schmidt orthonormalization for multiple exponents
ⓘ
choice of initial perturbation vectors ⓘ numerical integration of the system equations ⓘ |
| timePeriod | late 1970s ⓘ |
| usedFor |
characterizing chaos in dynamical systems
ⓘ
detecting sensitive dependence on initial conditions ⓘ estimating Lyapunov exponents ⓘ quantifying the rate of separation of nearby trajectories ⓘ |
| usedIn |
analysis of strange attractors
ⓘ
celestial mechanics ⓘ chaos detection in nonlinear dynamical systems ⓘ climate and atmospheric models ⓘ engineering control systems ⓘ study of Hamiltonian chaos ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Benettin algorithm Description of subject: The Benettin algorithm is a numerical method used in dynamical systems theory to estimate Lyapunov exponents, which quantify the rate of separation of nearby trajectories and indicate chaos.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.