Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
continuous dynamical systems
two-dimensional systems |
| gptkbp:field |
dynamical systems
|
| gptkbp:firstPublished |
1901
|
| https://www.w3.org/2000/01/rdf-schema#label |
Poincaré–Bendixson theorem
|
| gptkbp:implies |
chaotic behavior is impossible in two-dimensional continuous systems
|
| gptkbp:namedAfter |
gptkb:Henri_Poincaré
gptkb:Ivar_Bendixson |
| gptkbp:relatedTo |
partial differential equations
limit cycle phase portrait |
| gptkbp:sentence |
A nonempty compact limit set of a continuous dynamical system on the plane, which contains no fixed points, is a periodic orbit.
|
| gptkbp:usedIn |
gptkb:qualitative_theory_of_differential_equations
|
| gptkbp:bfsParent |
gptkb:Henri_Poincaré
gptkb:Dynamical_Systems |
| gptkbp:bfsLayer |
5
|