phenomenon 32.59 The solar system is chaotic

Rests on

• depends_on equation 32.46 eq:chaos-horizon ¶
• depends_on theorem 32.51 Kolmogorov–Arnold–Moser, quoted ¶
  • depends_on definition 32.50 Diophantine frequency vector ¶
    • depends_on proposition 32.49 The small-denominator obstruction ¶
      • depends_on equation 22.18 eq:ham-generating ¶
      • depends_on equation 23.52 eq:hj-angle-linear ¶
      • proves proof ch:15-nonlinear-dynamics-chaos@proof-17 ¶
  • depends_on theorem 23.31 Liouville–Arnold ¶
    • depends_on equation 22.41 eq:ham-poisson-bracket ¶
    • depends_on theorem 23.30 Motion in action–angle variables ¶
      • depends_on definition 23.28 Action variables ¶
        • depends_on definition 16.99 Abbreviated action ¶
        • depends_on definition 23.13 Additive separability ¶
      • depends_on proposition 22.18 The mixed generating functions ¶
        • depends_on definition 22.15 Canonical transformation ¶
        • depends_on equation 22.18 eq:ham-generating ¶ ↺
        • proves proof ch:05-hamiltonian-mechanics@proof-6 ¶
      • 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 ¶
      • proves proof ch:06-hamilton-jacobi@proof-8 ¶
    • depends_on theorem 24.21 Liouville ¶
      • depends_on definition 24.20 Liouville volume ¶
        • depends_on definition 13.102 Wedge product ¶
        • depends_on definition 24.8 Symplectic manifold ¶
        • depends_on theorem 24.12 Darboux ¶
      • depends_on proposition 7.105 Clairaut–Schwarz ¶
        • depends_on definition 7.20 Continuity at a point ¶
        • depends_on theorem 7.35 Mean value theorem ¶
        • proves proof ch:05-real-analysis@proof-64 ¶
      • depends_on theorem 24.16 The Hamiltonian flow preserves the symplectic form ¶
        • depends_on definition 24.14 Hamiltonian vector field ¶
        • depends_on definition 24.8 Symplectic manifold ¶ ↺
        • depends_on proposition 13.128 Cartan's magic formula ¶
        • proves proof ch:07-symplectic-geometry@proof-5 ¶
      • proves proof ch:07-symplectic-geometry@proof-8 ¶
    • proves proof ch:06-hamilton-jacobi@prooflink-1 ¶
• proves proof ch:15-nonlinear-dynamics-chaos@proof-20 ¶

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