theorem 24.38 Symplectic foliation, quoted

open in the book · parts/03-classical-mechanics/07-symplectic-geometry.tex:1264 · p. 863

Rests on

depends_on definition 24.37 Casimir function ¶
- depends_on definition 24.36 Poisson manifold ¶
  - depends_on definition 22.29 Poisson bracket ¶
    - depends_on definition 7.97 Partial derivative; gradient ¶
      - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on definition 5.15 Basis ¶
    - depends_on definition 22.14 Phase-space coordinate transformation ¶
      - depends_on definition 22.2 Hamiltonian ¶
  - depends_on equation 22.46 eq:ham-jacobi ¶
- depends_on proposition 24.15 Poisson bracket from the symplectic form ¶
  - depends_on definition 22.29 Poisson bracket ¶ ↺
  - depends_on definition 24.14 Hamiltonian vector field ¶
    - depends_on definition 24.8 Symplectic manifold ¶
      - depends_on definition 13.105 Closed form ¶
      - depends_on definition 13.98 $k$-form ¶
      - depends_on definition 24.2 Symplectic vector space ¶
    - depends_on equation 22.4 eq:ham-pdot ¶
    - depends_on equation 22.3 eq:ham-qdot ¶
  - depends_on equation 22.46 eq:ham-jacobi ¶ ↺
  - proves proof ch:07-symplectic-geometry@proof-4 ¶
depends_on definition 24.8 Symplectic manifold ¶ ↺
depends_on definition 24.36 Poisson manifold ¶ ↺

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type	direction	node	provenance	where
`depends_on`	→	Casimir function	declared	parts/03-classical-mechanics/07-symplectic-geometry.tex:1270
`depends_on`	→	Symplectic manifold	declared	parts/03-classical-mechanics/07-symplectic-geometry.tex:1270
`depends_on`	→	Poisson manifold	declared	parts/03-classical-mechanics/07-symplectic-geometry.tex:1270