Cartwright–Littlewood theory on nonlinear differential equations
E926679
Cartwright–Littlewood theory on nonlinear differential equations is a foundational body of work in dynamical systems that rigorously analyzed the complex, often chaotic behavior of solutions to nonlinear differential equations, particularly in the context of forced oscillations.
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theory
ⓘ
theory in dynamical systems ⓘ theory of nonlinear differential equations ⓘ |
| addresses |
bifurcation phenomena
ⓘ
existence of non-periodic recurrent behavior ⓘ existence of periodic solutions ⓘ |
| appliesTo |
forced nonlinear oscillators
ⓘ
non-autonomous differential equations ⓘ nonlinear second-order differential equations ⓘ |
| concerns |
irregular motions in forced systems
ⓘ
stability of solutions ⓘ transition from regular to chaotic behavior ⓘ |
| developedBy |
John Edensor Littlewood
NERFINISHED
ⓘ
Mary Cartwright NERFINISHED ⓘ |
| developedInPeriod |
1930s
ⓘ
1940s ⓘ |
| field |
applied mathematics
ⓘ
dynamical systems ⓘ nonlinear differential equations ⓘ |
| focusesOn |
existence of complicated invariant sets
ⓘ
long-term behavior of trajectories ⓘ qualitative behavior of solutions ⓘ sensitivity to initial conditions ⓘ |
| hasApplication |
engineering models of oscillations
ⓘ
mechanical vibration analysis ⓘ radio and electrical circuit models ⓘ |
| historicalContext |
early rigorous study of chaotic dynamics
ⓘ
precursor to modern chaos theory ⓘ |
| influenced |
modern dynamical systems theory
ⓘ
qualitative theory of differential equations ⓘ theory of strange attractors ⓘ |
| mainSubject |
chaotic behavior in differential equations
ⓘ
forced oscillations ⓘ nonlinear oscillations ⓘ |
| namedAfter |
John Edensor Littlewood
NERFINISHED
ⓘ
Mary Cartwright NERFINISHED ⓘ |
| notableFor |
analysis of highly nonlinear forced oscillators
ⓘ
early rigorous example of chaotic-like behavior in ODEs ⓘ |
| partOf |
history of chaos theory
ⓘ
history of dynamical systems ⓘ |
| relatedTo |
Poincaré–Bendixson theory
NERFINISHED
ⓘ
chaos theory ⓘ nonlinear dynamics ⓘ |
| usesMethod |
asymptotic analysis of solutions
ⓘ
qualitative phase-plane analysis ⓘ topological methods in analysis ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.