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.
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 NERFINISHED ⓘ |
| 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 NERFINISHED ⓘ |
| provides |
bounds on action variable variations
ⓘ
exponentially long stability estimates ⓘ long-time confinement in phase space ⓘ |
| relatesTo |
Arnold diffusion
NERFINISHED
ⓘ
Hamiltonian perturbation theory NERFINISHED ⓘ KAM theory NERFINISHED ⓘ long-term stability in celestial mechanics ⓘ |
| timePeriod | 1970s ⓘ |
| typicalEstimateForm | stability time bounded below by exp(const·ε^{-a}) for small ε GENERATED ⓘ |
| usedIn |
accelerator physics
ⓘ
astrodynamics ⓘ celestial mechanics ⓘ molecular dynamics ⓘ plasma physics ⓘ |
Referenced by (1)
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