remark 24.27 Fixing a scale, so that a ``ball'' means something

open in the book · parts/03-classical-mechanics/07-symplectic-geometry.tex:913 · p. 859

remark -- no derivation owed by its kind

Rests on

depends_on equation 22.56 eq:ham-symplectic-matrix ¶
depends_on remark 24.11 The SI dimension of every object in this chapter ¶
- depends_on proposition 24.10 The canonical form is symplectic and intrinsic ¶
  - depends_on definition 13.52 Differential; pushforward ¶
    - depends_on definition 13.49 Smooth map between manifolds ¶
      - depends_on definition 13.44 Atlas ¶
      - depends_on definition 13.45 Differentiable map on a topological space ¶
      - depends_on definition 13.48 Differentiable manifold ¶
    - depends_on definition 13.81 Vector on a manifold ¶
      - depends_on definition 13.71 Differentiable curve ¶
      - depends_on definition 13.45 Differentiable map on a topological space ¶ ↺
      - depends_on definition 13.48 Differentiable manifold ¶ ↺
  - depends_on definition 24.9 The canonical form on a cotangent bundle ¶
    - depends_on definition 13.103 Exterior derivative ¶
      - depends_on definition 13.98 $k$-form ¶
      - depends_on definition 13.102 Wedge product ¶
    - 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 lemma 13.107 Poincaré lemma ¶
    - depends_on definition 13.105 Closed form ¶ ↺
    - depends_on definition 13.106 Exact form ¶
      - depends_on definition 13.103 Exterior derivative ¶ ↺
      - depends_on definition 13.98 $k$-form ¶ ↺
    - depends_on equation 13.245 eq:mfd-nilpotency ¶
    - proves proof ch:11-manifolds-tensors-curvature@proof-21 ¶
  - proves proof ch:07-symplectic-geometry@proof-3 ¶
- depends_on remark 22.5 Units ¶
  - depends_on equation 22.1 eq:ham-hamiltonian ¶
  - depends_on equation 21.43 eq:lag-generalized-momentum ¶

Supports

depends_on definition 24.28 Ball and cylinder ¶
- depends_on definition 24.33 Symplectic capacity ¶
  - depends_on proposition 24.34 Capacities exist if and only if non-squeezing holds ¶
- depends_on example 24.29 A volume-preserving squeeze ¶
- depends_on proposition 24.30 Linear non-squeezing ¶
  - depends_on theorem 24.31 Gromov's non-squeezing theorem ¶
    - depends_on proposition 24.34 Capacities exist if and only if non-squeezing holds ¶ ↺
    - depends_on remark 24.35 What non-squeezing does and does not say about nature ¶
- depends_on theorem 24.31 Gromov's non-squeezing theorem ¶ ↺
depends_on definition 24.33 Symplectic capacity ¶ ↺

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:ham-symplectic-matrix	declared	parts/03-classical-mechanics/07-symplectic-geometry.tex:942
`depends_on`	→	The SI dimension of every object in this chapter	declared	parts/03-classical-mechanics/07-symplectic-geometry.tex:942
`depends_on`	←	Ball and cylinder	declared	parts/03-classical-mechanics/07-symplectic-geometry.tex:960
`depends_on`	←	Symplectic capacity	declared	parts/03-classical-mechanics/07-symplectic-geometry.tex:1117