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Liouville's theorem
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'''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 [[Harmonic functions#Liouville's theorem|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 [[Liouville_number#Liouville_numbers_and_transcendence|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) {{mathdab}}
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