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)

Topics referred to by the same term

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