Liouville's theorem
# Liouville's theorem

Liouville's theorem has various meanings, all mathematical results named after Joseph Liouville:

* In complex analysis, see Liouville's theorem (complex analysis)
   * There is also a related theorem on harmonic functions
* In conformal mappings, see Liouville's theorem (conformal mappings)
* In Hamiltonian mechanics, see Liouville's theorem (Hamiltonian) and Liouville–Arnold theorem
* In linear differential equations, see Liouville's formula
* In transcendence theory and diophantine approximations, the theorem that any Liouville number is transcendental
* In differential algebra, see Liouville's theorem (differential algebra)
* In differential geometry, see Liouville's equation
* In coarse-grained modelling, see Liouville's equation in coarse graining phase space in classical physics and fine graining of states in quantum physics (von Neumann density matrix)
