proposition 32.95 Intermittency: the scaling of the laminar phase

Rests on

• depends_on definition 32.38 Poincaré section and return map ¶
  • depends_on corollary 32.5 Trajectories do not cross ¶
    • depends_on proposition 32.4 The flow is a one-parameter group ¶
      • 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 9.8 Picard–Lindelöf ¶
        • depends_on definition 9.4 Lipschitz condition ¶
        • depends_on equation 9.3 eq:slt-ode-system ¶
        • depends_on lemma 9.6 Weierstrass $M$-test; uniform limits are continuous ¶
        • proves proof ch:07-odes-sturm-liouville@proof-2 ¶
      • proves proof ch:15-nonlinear-dynamics-chaos@proof-1 ¶
    • depends_on theorem 9.8 Picard–Lindelöf ¶ ↺
    • proves proof ch:15-nonlinear-dynamics-chaos@proof-2 ¶
  • depends_on definition 32.3 Dynamical system, phase space, flow ¶ ↺
• depends_on proposition 32.23 Saddle-node bifurcation ¶
  • depends_on definition 32.22 Bifurcation ¶
    • depends_on definition 32.3 Dynamical system, phase space, flow ¶ ↺
    • depends_on theorem 32.15 Hartman–Grobman, restated from Part II ¶
      • depends_on definition 32.12 Linearization ¶
        • depends_on definition 32.10 Fixed point ¶
        • depends_on theorem 7.38 Taylor's theorem with Lagrange remainder ¶
      • depends_on definition 6.7 Homeomorphism ¶
        • depends_on definition 3.47 Bijective map ¶
        • depends_on definition 3.51 Inverse map ¶
        • depends_on definition 6.6 Continuous map ¶
      • depends_on theorem 9.32 Hartman–Grobman; quoted ¶
        • depends_on definition 9.30 Hyperbolic equilibrium ¶
        • depends_on definition 6.7 Homeomorphism ¶ ↺
        • depends_on theorem 9.23 Solution of a constant-coefficient system ¶
  • depends_on theorem 32.13 Linear stability ¶
    • depends_on definition 32.12 Linearization ¶ ↺
    • depends_on theorem 5.77 Criterion for diagonalizability ¶
      • depends_on definition 5.76 Diagonalizable operator ¶
        • depends_on definition 5.56 Endomorphism ¶
        • 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 proposition 5.75 Eigenvectors for distinct eigenvalues are independent ¶
        • depends_on definition 5.69 Eigenvector, eigenvalue, eigenspace ¶ ↺
        • depends_on definition 5.14 Linear independence ¶
        • 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-7 ¶
• proves proof ch:15-nonlinear-dynamics-chaos@proof-32 ¶

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