nLab
Liouville integrable system

Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Symplectic geometry

Contents

Idea

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.

Definition

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

Revised on October 15, 2012 20:46:54 by Zoran Škoda (161.53.130.104)