Nekhoroshev theory
E1041765
Nekhoroshev theory is a result in Hamiltonian dynamical systems that provides exponentially long stability estimates for nearly integrable systems under small perturbations.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Nekhoroshev theory canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T13443970 — 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: Nekhoroshev theory Context triple: [Kolmogorov–Arnold–Moser theory, relatedTo, Nekhoroshev theory]
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A.
Kolmogorov–Arnold–Moser theory
Kolmogorov–Arnold–Moser theory is a fundamental result in dynamical systems that explains the persistence of quasi-periodic motions in nearly integrable Hamiltonian systems under small perturbations.
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B.
Liouville–Arnold theorem
The Liouville–Arnold theorem is a fundamental result in Hamiltonian mechanics that guarantees the integrability of a system with sufficiently many conserved quantities and describes its motion as quasi-periodic on invariant tori in phase space.
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C.
Liouville's theorem in Hamiltonian mechanics
Liouville's theorem in Hamiltonian mechanics states that the phase-space volume occupied by an ensemble of systems evolving under Hamiltonian dynamics is conserved over time, implying incompressible flow in phase space.
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D.
Poincaré recurrence theorem
The Poincaré recurrence theorem is a fundamental result in dynamical systems and ergodic theory stating that certain systems will, after a sufficiently long but finite time, return arbitrarily close to their initial state.
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E.
Kovalevskaya integral
The Kovalevskaya integral is an additional conserved quantity that makes the motion of the Kovalevskaya top exactly integrable in classical rigid body dynamics.
- 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: Nekhoroshev theory Target entity description: Nekhoroshev theory is a result in Hamiltonian dynamical systems that provides exponentially long stability estimates for nearly integrable systems under small perturbations.
-
A.
Kolmogorov–Arnold–Moser theory
Kolmogorov–Arnold–Moser theory is a fundamental result in dynamical systems that explains the persistence of quasi-periodic motions in nearly integrable Hamiltonian systems under small perturbations.
-
B.
Liouville–Arnold theorem
The Liouville–Arnold theorem is a fundamental result in Hamiltonian mechanics that guarantees the integrability of a system with sufficiently many conserved quantities and describes its motion as quasi-periodic on invariant tori in phase space.
-
C.
Liouville's theorem in Hamiltonian mechanics
Liouville's theorem in Hamiltonian mechanics states that the phase-space volume occupied by an ensemble of systems evolving under Hamiltonian dynamics is conserved over time, implying incompressible flow in phase space.
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D.
Painlevé conjecture in celestial mechanics
The Painlevé conjecture in celestial mechanics is a hypothesis about the possible occurrence of non-collision singularities—where bodies in an N-body gravitational system exhibit infinite behavior in finite time without actually colliding.
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E.
Poincaré recurrence theorem
The Poincaré recurrence theorem is a fundamental result in dynamical systems and ergodic theory stating that certain systems will, after a sufficiently long but finite time, return arbitrarily close to their initial state.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theory
ⓘ
result in Hamiltonian dynamics ⓘ stability theory ⓘ |
| appliesTo |
analytic Hamiltonian systems
ⓘ
nearly integrable Hamiltonian systems ⓘ small perturbations of integrable systems ⓘ |
| assumes |
analyticity of the Hamiltonian
ⓘ
non-degeneracy conditions ⓘ steepness conditions on the unperturbed Hamiltonian ⓘ |
| characteristicTimeScale | exponentially long in inverse perturbation size ⓘ |
| comparedTo |
KAM theory gives quasi-periodic invariant tori
ⓘ
Nekhoroshev estimates allow slow drift but over exponentially long times ⓘ |
| concerns |
exponential estimates in perturbation parameter
ⓘ
long-time behavior of nearly integrable systems ⓘ stability of action-angle variables ⓘ |
| developedBy | Nikolay Nekhoroshev ⓘ |
| field |
Hamiltonian dynamical systems
ⓘ
dynamical systems ⓘ mathematical physics ⓘ perturbation theory ⓘ symplectic geometry ⓘ |
| generalizationOf | classical perturbation stability results ⓘ |
| hasConsequence | practical long-term predictability for small perturbations ⓘ |
| implies |
effective stability over very long but finite times
ⓘ
slow diffusion of actions under small perturbations ⓘ |
| influenced |
modern studies of Arnold diffusion
ⓘ
stability analysis of the Solar System ⓘ |
| involves |
exponential smallness estimates
ⓘ
multi-scale analysis in action space ⓘ normal form transformations ⓘ resonant and non-resonant domains ⓘ |
| mathematicalNature | quantitative stability theorem ⓘ |
| namedAfter | Nikolay Nekhoroshev ⓘ |
| provides |
bounds on action variable variations
ⓘ
exponentially long stability estimates ⓘ long-time confinement in phase space ⓘ |
| relatesTo |
Arnold diffusion
ⓘ
Hamiltonian perturbation theory ⓘ KAM theory ⓘ
linked to:
Kolmogorov–Arnold–Moser theory
long-term stability in celestial mechanics ⓘ |
| timePeriod | 1970s ⓘ |
| typicalEstimateForm | stability time bounded below by exp(const·ε^{-a}) for small ε ⓘ |
| usedIn |
accelerator physics
ⓘ
astrodynamics ⓘ celestial mechanics ⓘ molecular dynamics ⓘ plasma physics ⓘ |
How these facts were elicited
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Instruction
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Subject: Nekhoroshev theory Description of subject: Nekhoroshev theory is a result in Hamiltonian dynamical systems that provides exponentially long stability estimates for nearly integrable systems under small perturbations.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.