Liouville theorem

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• 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

• 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-Gleichung — Die Liouville Gleichung, nach Joseph Liouville, ist eine Beschreibung der zeitlichen Entwicklung eines physikalischen Systems in der statistischen Mechanik, im Hamilton Formalismus der klassischen Mechanik und in der Quantenmechanik, dort auch… …   Deutsch Wikipedia

• Liouville's theorem — has various meanings, all mathematical results named after Joseph Liouville:*In complex analysis, see Liouville s theorem (complex analysis). *In conformal mappings, see Liouville s theorem (conformal mappings). *In Hamiltonian mechanics, see… …   Wikipedia

• Liouville-Gleichung —   [lju vil ; nach J. Liouville], partielle Differenzialgleichung der statistischen Mechanik für die Verteilungsfunktion f(N) (r1,. .., rN; pN …   Universal-Lexikon

• 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 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'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, 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 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 dynamical system — In classical mechanics, a Liouville dynamical system is an exactly soluble dynamical system in which the kinetic energy T and potential energy V can be expressed in terms of the s generalized coordinates q as followscite journal | last =… …   Wikipedia