proposition 32.65 Fixed points of the Lorenz system and their stability

Rests on

• depends_on equation 32.36 eq:chaos-lorenz ¶
• depends_on theorem 32.13 Linear stability ¶
  • depends_on definition 32.12 Linearization ¶
    • depends_on definition 32.10 Fixed point ¶
      • depends_on definition 32.3 Dynamical system, phase space, flow ¶
        • depends_on definition 13.82 Vector field ¶
        • depends_on definition 9.1 Ordinary differential equation ¶
    • depends_on theorem 7.38 Taylor's theorem with Lagrange remainder ¶
      • depends_on proposition 7.30 Leibniz rule ¶
        • depends_on definition 7.12 Product of functions ¶
        • depends_on equation 7.14 eq:ana-derivh ¶
        • depends_on proposition 7.27 Differentiable implies continuous ¶
        • depends_on proposition 7.6 Algebra of limits ¶
        • proves proof ch:05-real-analysis@proof-14 ¶
      • depends_on theorem 7.34 Rolle ¶
        • depends_on lemma 7.33 Fermat: interior extremum ¶
        • depends_on theorem 7.24 Extreme value theorem ¶
        • proves proof ch:05-real-analysis@proof-18 ¶
      • proves proof ch:05-real-analysis@proof-22 ¶
  • depends_on theorem 5.77 Criterion for diagonalizability ¶
    • depends_on definition 5.76 Diagonalizable operator ¶
      • depends_on definition 5.56 Endomorphism ¶
        • depends_on definition 5.37 Linear transformation ¶
      • depends_on equation 5.74 eq:lin-matrix-rep ¶
    • depends_on definition 5.69 Eigenvector, eigenvalue, eigenspace ¶
      • depends_on definition 5.56 Endomorphism ¶ ↺
      • depends_on definition 5.39 Kernel, image, nullity, rank ¶
        • depends_on definition 5.37 Linear transformation ¶ ↺
        • depends_on definition 5.7 Vector subspace ¶
        • proves proof ch:03-linear-algebra-representations@proof-12 ¶
    • depends_on proposition 5.75 Eigenvectors for distinct eigenvalues are independent ¶
      • depends_on definition 5.69 Eigenvector, eigenvalue, eigenspace ¶ ↺
      • depends_on definition 5.14 Linear independence ¶
        • depends_on definition 5.5 Linear combination ¶
      • proves proof ch:03-linear-algebra-representations@proof-29 ¶
    • proves proof ch:03-linear-algebra-representations@proof-30 ¶
  • proves proof ch:15-nonlinear-dynamics-chaos@proof-4 ¶
• proves proof ch:15-nonlinear-dynamics-chaos@proof-23 ¶

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