Poincaré–Bendixson theorem
Teorema de Poincaré-Bendixson
- Date
- 1901 · confidence low
- Place
- Stockholm, Sweden
- Credited to
- Ivar Bendixson y Henri Poincaré
- Field
- Knowledge & symbols
What was discovered
A theorem on continuous dynamical systems on the plane, cylinder, or sphere describing the long-term behavior of orbits and ruling out chaos in two dimensions, stated by Henri Poincaré and rigorously proved by Ivar Bendixson.
What it led to
- classification of possible limit behaviors of planar systems (fixed points, limit cycles)
- key tool in the study of nonlinear oscillators
- explanation of why deterministic chaos requires at least three dimensions
- basis of the qualitative theory of differential equations