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.

Type

Journal article

Intellectual base

Primary research

Year

1838

Link

https://www.numdam.org/item/JMPA_1838_1_3__342_0.pdf

Cited from

physics

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.

• 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.

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