Dynamical systems and ergodic theory Hamiltonian dynamics Concept
Integrable system
Summary
An integrable system is a Hamiltonian system with as many independent conserved quantities in involution as it has degrees of freedom. Such a system can be solved, in principle, by quadratures, and its motions on compact regular level sets are quasi-periodic motions on invariant tori. The word is also used for infinite-dimensional systems, such as the Korteweg–De Vries equation. These have infinitely many conserved quantities and can be solved by inverse scattering. Integrable systems are the starting point of perturbation theory, where the question is what survives when the system is slightly changed.
Where this leads
6 pages build on this one.
Further reading
About this page
| Tag | N0N7CMRCMH |
|---|---|
| URI | m2://N0N7CMRCMH |
| Kind | concept |
| Writing | W0 stub |
| MSC | 37J35, 70H06, 37K10 |
| Specializes | Hamiltonian system |
| Same as |
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Results about this
- Kolmogorov–Arnold–Moser theorem
- Fermi–Pasta–Ulam–Tsingou problem
- Liouville–Arnold theorem
- Nekhoroshev estimates
Used by
- Kolmogorov–Arnold–Moser theorem
- Arnold diffusion
- Fermi–Pasta–Ulam–Tsingou problem
- Liouville–Arnold theorem
- Nekhoroshev estimates