Liouville's theorem (Hamiltonian)

:A separate article is about Liouville's theorem in complex analysis: see Liouville's theorem (complex analysis).

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

In mathematical physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics. It asserts that the phase-space distribution function is constant along the trajectories of the system - that is that the density of system points in the vicinity of a given system point travelling through phase-space is constant with time..

Related Topics:
Mathematical physics - Joseph Liouville - Statistical - Hamiltonian mechanics - Phase-space

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Liouville's theorem is also important in the study of symplectic topology, where it is formulated rather differently.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~