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Symplectic Geometry of Phase Space
Symplectic Geometry of Phase Space
foundations +4 more results +9 more equations depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) notation 24.1: not:sym-notation 24.1 notation definition 24.2: Symplectic vector space 24.2 Symplectic vecto… definition 24.4: Symplectic group 24.4 Symplectic group definition 24.8: Symplectic manifold 24.8 Symplectic manif… definition 24.9: The canonical form on a cotangent bundle 24.9 The canonical fo… definition 24.14: Hamiltonian vector field 24.14 Hamiltonian vect… definition 24.17: Symplectomorphism 24.17 Symplectomorphism definition 24.20: Liouville volume 24.20 Liouville volume definition 24.28: Ball and cylinder 24.28 Ball and cylinder definition 24.33: Symplectic capacity 24.33 Symplectic capac… definition 24.36: Poisson manifold 24.36 Poisson manifold definition 24.37: Casimir function 24.37 Casimir function definition 24.40: Lie–Poisson bracket 24.40 Lie–Poisson brac… proposition 24.3: Even dimension and the canonical basis 24.3 Even dimension a… proposition 24.5: Properties of the symplectic group 24.5 Properties of th… proposition 24.10: The canonical form is symplectic and intrinsic 24.10 The canonical fo… theorem 24.12: Darboux 24.12 Darboux proposition 24.15: Poisson bracket from the symplectic form 24.15 Poisson bracket… theorem 24.16: The Hamiltonian flow preserves the symplectic form 24.16 The Hamiltonian… theorem 24.18: Symplectic form of the transformation condition 24.18 Symplectic form… corollary 24.19: Canonical transformations preserve phase volume 24.19 Canonical transf… theorem 24.21: Liouville 24.21 Liouville theorem 24.23: Poincaré–Cartan integral invariant 24.23 Poincaré–Cartan… theorem 24.24: Poincaré recurrence 24.24 Poincaré recurre… proposition 24.30: Linear non-squeezing 24.30 Linear non-squee… theorem 24.31: Gromov's non-squeezing theorem 24.31 Gromov's non-squ… equation 24.3: eq:sym-canonical-forms eq. (24.3) equation 24.5: eq:sym-hamiltonian-field eq. (24.5) equation 24.6: eq:sym-hamiltonian-field-coords eq. (24.6) equation 24.7: eq:sym-bracket eq. (24.7) equation 24.8: eq:sym-bracket-homomorphism eq. (24.8) equation 24.19: eq:sym-omega-euclid eq. (24.19) equation 24.34: eq:sym-prequantum-condition eq. (24.34) equation 24.35: eq:sym-prequantum-local eq. (24.35) The chain of Symplectic Geometry of Phase Space: 34 of 47 objects, read left to right from what the chapter assumes to what tests it. Solid lines are declared logical edges, dashed ones were inferred from the structure of the source. Click any node to open its own chain.