lemma A.546 The Hamiltonian fields of the integrals
open in the book ·
appendices/A-long-proofs.tex:26528
· p. 3058
Rests on
- depends_on equation A.844 eq:app-hj-liouville-arnold-involution ¶
- depends_on equation 24.8 eq:sym-bracket-homomorphism ¶
- depends_on equation 24.5 eq:sym-hamiltonian-field ¶
- proves proof app:A-long-proofs@proof-330 ¶
Supports
-
depends_on
lemma A.548
The joint flow is a translation action on the level set
¶
- depends_on corollary A.553 Quasi-periodic motion ¶
-
depends_on
lemma A.549
The action is transitive
¶
-
depends_on
proposition A.552
The component is a torus
¶
- depends_on corollary A.553 Quasi-periodic motion ¶ ↺
-
depends_on
definition A.554
Actions on the torus
¶
- depends_on lemma A.555 The actions are well defined ¶
- depends_on proposition A.556 The Jacobian of the actions is the lattice matrix ¶
- depends_on proposition A.556 The Jacobian of the actions is the lattice matrix ¶ ↺
-
depends_on
proposition A.552
The component is a torus
¶
- depends_on proposition A.552 The component is a torus ¶ ↺
-
depends_on
proposition A.547
The components of the level set are the leaves of
an integrable distribution
¶
- depends_on lemma A.549 The action is transitive ¶ ↺
- depends_on lemma A.555 The actions are well defined ¶ ↺
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | eq:app-hj-liouville-arnold-involution | declared | appendices/A-long-proofs.tex:26539 |
depends_on |
→ | eq:sym-bracket-homomorphism | declared | appendices/A-long-proofs.tex:26539 |
depends_on |
→ | eq:sym-hamiltonian-field | declared | appendices/A-long-proofs.tex:26539 |
depends_on |
← | The joint flow is a translation action on the level set | declared | appendices/A-long-proofs.tex:26624 |
depends_on |
← | The components of the level set are the leaves of an integrable distribution | declared | appendices/A-long-proofs.tex:26576 |
proves |
← | app:A-long-proofs@proof-330 | declared | appendices/A-long-proofs.tex:26543 |