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)