Painlevé conjecture in celestial mechanics
E1041303
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Painlevé conjecture in celestial mechanics canonical | 1 |
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
conjecture in dynamical systems
ⓘ
mathematical conjecture ⓘ scientific conjecture ⓘ |
| appliesTo | N-body problem with N ≥ 3 ⓘ |
| assumes |
Newtonian gravity
NERFINISHED
ⓘ
point-mass particles ⓘ |
| concerns |
N-body gravitational systems
ⓘ
Newtonian gravitational interaction ⓘ equations of motion in the N-body problem ⓘ finite-time singularities ⓘ non-collision singularities ⓘ |
| contrastsWith | conjectures that all singularities are collision singularities ⓘ |
| describes |
possibility of infinite behavior in finite time without collisions
ⓘ
trajectories with unbounded velocities in finite time ⓘ |
| field |
celestial mechanics
ⓘ
classical mechanics ⓘ dynamical systems theory ⓘ gravitational N-body problem ⓘ mathematical physics ⓘ |
| formalizes | question of whether all singularities in N-body motion are due to collisions ⓘ |
| hasKeyConcept |
analytic continuation of solutions
ⓘ
finite-time blow-up ⓘ maximal interval of existence of solutions ⓘ non-collision singularity ⓘ |
| historicalContext | early 20th century celestial mechanics ⓘ |
| influenced |
later work on singularities in Hamiltonian systems
ⓘ
research on non-collision singularities in higher-dimensional N-body problems ⓘ |
| mathematicalSetting | ordinary differential equations of Newtonian N-body motion ⓘ |
| motivatedBy |
classification of singularities of N-body trajectories
ⓘ
study of singularities in the three-body problem ⓘ |
| namedAfter | Paul Painlevé NERFINISHED ⓘ |
| relatedProblem |
classification of all possible singular behaviors in gravitational N-body systems
ⓘ
existence of complete solutions for all time in the N-body problem ⓘ |
| relatedTo |
collision singularities in the N-body problem
ⓘ
global behavior of solutions of differential equations ⓘ qualitative theory of differential equations ⓘ singularity formation in dynamical systems ⓘ stability of the solar system ⓘ |
| requires | analysis of asymptotic behavior of trajectories near singular times ⓘ |
| status | partially resolved in specific N-body configurations ⓘ |
| typeOfSingularityConsidered | non-collision finite-time singularity GENERATED ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.