Liouville's theorem - AbsoluteAstronomy.com

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

Joseph Liouville

- Life and work :Liouville graduated from the École Polytechnique in 1827. After some years as an assistant at various institutions including the Ecole Centrale Paris, he was appointed as professor at the École Polytechnique in 1838...

In complex analysis, see Liouville's theorem (complex analysis)
Liouville's theorem (complex analysis)
In complex analysis, Liouville's theorem, named after Joseph Liouville, states that every bounded entire function must be constant. That is, every holomorphic function f for which there exists a positive number M such that |f| ≤ M for all z in C is constant.The theorem is considerably improved by...

; 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)
Liouville's theorem (Hamiltonian)
In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics...

.
In linear differential equations, see Liouville's formula
Liouville's formula
In mathematics, Liouville's formula is an equation that expresses the determinant of a square-matrix solution of a first-order system of homogeneous linear differential equations in terms of the sum of the diagonal coefficients of the system...

.
In number theory:
- The theorem that any Liouville number is transcendental
- The lemma involved on diophantine approximation
  Diophantine approximation
  In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers....
In differential algebra, see Liouville's theorem (differential algebra)
Liouville's theorem (differential algebra)
In mathematics, Liouville's theorem, originally formulated by Joseph Liouville in the 1830s and 1840s, places an important restriction on antiderivatives that can be expressed as elementary functions....
In differential geometry, see Liouville's equation

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