Note sur la Théorie de la Variation des constantes arbitraires.¶
Liouville, J. (1838). Note sur la Théorie de la Variation des constantes arbitraires. Journal de Mathématiques Pures et Appliquées, 3, 342-349.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Ensemble
- Liouville's theorem
This sourceProves conservation of phase-space density (the divergence of the phase-space velocity field vanishes), the measure-theoretic foundation of ensemble theory.
Supported in partVerified against the work's full text
Liouville's 1838 note proves the determinant-derivative identity underlying the theorem, but in ODE variation-of-constants form with no phase-space or ensemble language.
“en sorte que le dénominateur u est alors indépendant de t”
- Liouville's theorem
- Phase Space
- the symplectic structure ω = dq ∧ dp is the fundamental geometric invariant.
This sourceEstablishes conservation of phase-space density under Hamiltonian flow (Liouville's theorem); foundational for measure-theoretic grounding of ensemble theory; shows that phase-space probability density is preserved by dynamical evolution.
- the symplectic structure ω = dq ∧ dp is the fundamental geometric invariant.
Verification¶
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Registry ID ref:32aaddf6fdac · see in the full table