example A.557 The check that fixes the convention

open in the book · appendices/A-long-proofs.tex:26887 · p. 3061

example -- no derivation owed by its kind

Rests on

depends_on equation 23.57 eq:hj-adiabatic-dIdE ¶
depends_on proposition A.556 The Jacobian of the actions is the lattice matrix ¶
- depends_on definition A.554 Actions on the torus ¶
  - depends_on equation 23.49 eq:hj-action-variable ¶
  - depends_on equation 24.3 eq:sym-canonical-forms ¶
  - depends_on proposition A.552 The component is a torus ¶
    - depends_on lemma A.548 The joint flow is a translation action on the level set ¶
      - depends_on lemma A.546 The Hamiltonian fields of the integrals ¶
      - depends_on proposition 13.131 Commuting fields have commuting flows ¶
      - depends_on theorem 13.125 Existence, uniqueness and smoothness of the flow ¶
      - proves proof app:A-long-proofs@proof-332 ¶
    - depends_on lemma A.549 The action is transitive ¶
      - depends_on corollary A.292 Inverse function theorem ¶
      - depends_on lemma A.548 The joint flow is a translation action on the level set ¶ ↺
      - depends_on proposition A.547 The components of the level set are the leaves of an integrable distribution ¶
      - proves proof app:A-long-proofs@proof-333 ¶
    - depends_on theorem A.550 Quoted: discrete subgroups of a real vector space ¶
      - depends_on definition 4.21 Group ¶
      - depends_on definition 6.9 Compact set ¶
    - proves proof app:A-long-proofs@proof-334 ¶
- depends_on proposition A.552 The component is a torus ¶ ↺
- depends_on proposition 22.18 The mixed generating functions ¶
  - depends_on definition 22.15 Canonical transformation ¶
    - depends_on definition 22.14 Phase-space coordinate transformation ¶
      - depends_on definition 22.2 Hamiltonian ¶
    - depends_on definition 21.45 Action ¶
      - depends_on definition 16.96 Action; Hamilton's principle ¶
      - depends_on equation 21.37 eq:lag-lagrangian ¶
    - depends_on theorem 22.6 Hamilton's equations ¶
      - depends_on definition 22.2 Hamiltonian ¶ ↺
      - depends_on equation 21.39 eq:lag-el-conservative ¶
      - depends_on equation 21.43 eq:lag-generalized-momentum ¶
      - proves proof ch:05-hamiltonian-mechanics@proof-2 ¶
  - depends_on equation 22.18 eq:ham-generating ¶
  - proves proof ch:05-hamiltonian-mechanics@proof-6 ¶
- proves proof app:A-long-proofs@proof-337 ¶

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type	direction	node	provenance	where
`depends_on`	→	eq:hj-adiabatic-dIdE	declared	appendices/A-long-proofs.tex:26896
`depends_on`	→	The Jacobian of the actions is the lattice matrix	declared	appendices/A-long-proofs.tex:26896