MANIFOLD (Invariant)
Charles François (2004). MANIFOLD (Invariant), International Encyclopedia of Systems and Cybernetics, 2(1): 1998.
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(1) |
| ID | ◀ 1998 ▶ |
| Object type | Discipline oriented, Methodology or model |
- “A surface containing the phase space of a dynamical system which has the property that orbits starting on the surface remain on the surface throughout the course of their dynamical evolution” (S. WIGGINS, 1988).
WIGGINS adds: “…the set of orbits which approach or recede from an invariant manifold M asymptotically in time under certain conditions are also invariant manifolds which are called the stable and unstable manifolds respectively, of M. Knowledge of the invariant manifolds of a dynamical system as well of the interactions of their respective stable and unstable manifolds is absolutely crucial in order to obtain a complete understanding of the global dynamics” (Ibid).
While previous to and independent of the study of chaos, the subject has now become an indispensable tool for the modelization of turbulence and chaos in mathematicaL terms.