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 ( z )| ≤ M for all… … Wikipedia
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. It asserts that the phase space distribution function is constant along the trajectories… … Wikipedia
Liouville's theorem (conformal mappings) — In mathematics, Liouville s theorem is a theorem about conformal mappings in Euclidean space. It states that any conformal mapping on a domain of R n , where n > 2, can be expressed as a composition of translations, similarities, orthogonal… … Wikipedia
liouville's theorem — (ˈ)lyü|vēlz noun Usage: usually capitalized L Etymology: after Joseph Liouville died 1882 French mathematician : a theorem in fluid dynamics: the density of any selected part of a stream of fluid that does no work and that has no work done on it… … Useful english dictionary
Liouville's theorem — Math. the theorem that every function of a complex variable, bounded and differentiable for all finite values of the variable, is a constant function. [named after J. LIOUVILLE] * * * … Universalium
Liouville number — In number theory, a Liouville number is a real number x with the property that, for every positive integer n, there exist integers p and q with q > 1 and such that A Liouville number can thus be approximated quite closely by a sequence of… … Wikipedia
Liouville, Joseph — ▪ French mathematician born March 24, 1809, Saint Omer, France died September 8, 1882, Paris French mathematician known for his work in analysis, differential geometry, and number theory and for his discovery of transcendental numbers i.e … Universalium
Liouville's equation — For Liouville s equation in dynamical systems, see Liouville s theorem (Hamiltonian). In differential geometry, Liouville s equation, named after Joseph Liouville, is the equation satisfied by the conformal factor f of a metric f^2 (dx^2 + dy^2)… … Wikipedia
Liouville-Gleichung — [lju vil ; nach J. Liouville], partielle Differenzialgleichung der statistischen Mechanik für die Verteilungsfunktion f(N) (r1,. .., rN; pN … Universal-Lexikon
Liouville-Theorem — Der Satz von Liouville (auch Liouville Theorem genannt, nach Joseph Liouville) ist eine direkte Folge aus der Liouville Gleichung und besagt, dass das von benachbarten Trajektorien im Phasenraum eingeschlossene (mehrdimensionale) Volumen konstant … Deutsch Wikipedia
