Integrable System
In mathematics and physics, there are various distinct notions that are referred to under the name of integrable systems.
In the general theory of differential systems, there is Frobenius integrability, which refers to overdetermined systems. In the classical theory of Hamiltonian dynamical systems, there is the notion of Liouville integrability. More generally, in differentiable dynamical systems integrability relates to the existence of foliations by invariant submanifolds within the phase space. Each of these notions involves an application of the idea of foliations, but they do not coincide. There are also notions of complete integrability, or exact solvability in the setting of quantum systems and statistical mechanical models. Integrability can often be traced back to the algebraic geometry of differential operators.
Read more about Integrable System: Frobenius Integrability (overdetermined Differential Systems), General Dynamical Systems, Hamiltonian Systems and Liouville Integrability, Action-angle Variables, The Hamilton–Jacobi Approach, Solitons and Inverse Spectral Methods, Quantum Integrable Systems, Exactly Solvable Models, List of Some Well-known Classical Integrable Systems
Famous quotes containing the word system:
“To care for the quarrels of the past, to identify oneself passionately with a cause that became, politically speaking, a losing cause with the birth of the modern world, is to experience a kind of straining against reality, a rebellious nonconformity that, again, is rare in America, where children are instructed in the virtues of the system they live under, as though history had achieved a happy ending in American civics.”
—Mary McCarthy (1912–1989)