nLab Liouville integrable system




physics, mathematical physics, philosophy of physics

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theory (physics), model (physics)

experiment, measurement, computable physics

Symplectic geometry



What is called Liouville integrability is one formalization of the notion of classical integrable system in physics.

A physical system is called Liouville integrable if it admits canonical coordinates and canonical momenta which are generated from the flow of a maximal set of commuting Hamiltonians.


A physical system given by a phase space symplectic manifold (X,ω)(X, \omega) and equipped with a Hamiltonian H 0C (C)H_0 \in C^\infty(C) (generating time evolution) is said to be Liouville integrable or to be an integrable system in the sens of Liouville if

Last revised on October 15, 2012 at 20:46:54. See the history of this page for a list of all contributions to it.