equation 9.3 eq:slt-ode-system

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Supports

• depends_on definition A.438 Momentum variable and the accessory system ¶
  • depends_on lemma A.439 Existence, uniqueness, and the structure of the zeros ¶
    • depends_on lemma A.442 The Wronskian of the accessory equation is constant ¶
      • depends_on definition A.467 Green function of the shifted problem ¶
        • depends_on lemma A.468 The kernel is well defined, symmetric and Lipschitz ¶
        • depends_on theorem A.469 The Green operator inverts $L_{K}$ ¶
      • depends_on theorem A.443 Sturm separation theorem ¶
    • depends_on theorem A.441 Continuous dependence on the data and on the initial point ¶
      • depends_on corollary A.445 Displacing the initial point ¶
• depends_on theorem 9.8 Picard–Lindelöf ¶
  • depends_on corollary 32.5 Trajectories do not cross ¶
    • depends_on definition 32.29 Limit cycle ¶
      • depends_on phenomenon 32.35 Self-sustained oscillation ¶
        • depends_on phenomenon 32.37 Frequency demultiplication and the first heard chaos ¶
    • depends_on definition 32.38 Poincaré section and return map ¶
      • depends_on definition 32.91 The circle map ¶
        • depends_on proposition 32.93 The circle map loses invertibility at $K=1$ ¶
      • depends_on example 32.70 The Hénon map ¶
      • depends_on proposition 32.93 The circle map loses invertibility at $K=1$ ¶ ↺
      • depends_on proposition 32.95 Intermittency: the scaling of the laminar phase ¶
      • depends_on proposition 32.39 Stability of a periodic orbit ¶
        • depends_on phenomenon 32.87 Universal period doubling ¶
        • depends_on proposition 32.84 Fixed points and the first period doubling ¶
    • depends_on theorem 32.30 Poincaré–Bendixson, restated from Part II ¶
      • depends_on corollary 32.32 No chaos in a planar flow ¶
  • depends_on corollary 9.9 Linear equations: existence on the whole interval ¶
    • depends_on definition 9.37 Fundamental matrix ¶
      • depends_on proposition 9.38 Liouville's formula ¶
        • depends_on corollary 9.41 Hill's equation ¶
        • depends_on theorem 9.39 Floquet ¶
      • depends_on theorem 9.39 Floquet ¶ ↺
    • depends_on lemma A.439 Existence, uniqueness, and the structure of the zeros ¶ ↺
    • depends_on proposition 20.9 Linear resistance: exact motion, and the lost range ¶
      • depends_on remark 20.11 What has no closed form, and what to do about it ¶
    • depends_on proposition 9.103 The positive zeros and their spacing ¶
    • depends_on proposition 9.18 The linear equation: integrating factor ¶
      • depends_on proposition 9.87 The distinguished limit, and which end carries the layer ¶
        • depends_on proposition 9.88 The model problem, and the error of the composite ¶
    • depends_on theorem A.74 Flow of a time-dependent vector field ¶
      • depends_on theorem 13.125 Existence, uniqueness and smoothness of the flow ¶
        • depends_on lemma A.548 The joint flow is a translation action on the level set ¶
        • depends_on lemma A.567 The differential of the momentum map along the orbit ¶
        • depends_on proposition 13.131 Commuting fields have commuting flows ¶
        • depends_on proposition 13.132 Simultaneous straightening of commuting fields ¶
        • depends_on theorem 13.137 Commuting complete fields on a compact manifold ¶
    • depends_on theorem 9.23 Solution of a constant-coefficient system ¶
      • depends_on corollary 9.25 Normal modes of a diagonalizable system ¶
        • depends_on corollary 9.27 Linear stability ¶
        • depends_on proposition 9.29 The planar classification ¶
      • depends_on proposition 9.87 The distinguished limit, and which end carries the layer ¶ ↺
      • depends_on proposition 9.31 Lyapunov's first method: asymptotic stability ¶
      • depends_on proposition 9.43 The unmodulated line, and the feet of the tongues ¶
      • depends_on theorem 9.32 Hartman–Grobman; quoted ¶
        • depends_on theorem 32.15 Hartman–Grobman, restated from Part II ¶
      • depends_on theorem 9.26 Structure of the solutions ¶
        • depends_on corollary 9.27 Linear stability ¶ ↺
    • depends_on theorem 9.13 Dimension of the solution space ¶
      • depends_on definition 9.37 Fundamental matrix ¶ ↺
      • depends_on proposition 28.18 The three regimes ¶
      • depends_on proposition 28.4 General solution and isochronism ¶
        • depends_on phenomenon 28.9 Isochronism of the small-amplitude pendulum ¶
      • depends_on proposition 9.106 The modified series and what it does not do ¶
      • depends_on proposition 9.28 The scalar constant-coefficient equation ¶
        • depends_on proposition 9.88 The model problem, and the error of the composite ¶ ↺
      • depends_on proposition 9.16 Wronskian test for independence ¶
  • depends_on proposition 32.4 The flow is a one-parameter group ¶
    • depends_on corollary 32.5 Trajectories do not cross ¶ ↺
  • depends_on proposition 10.16 Cauchy's characteristic strips ¶
  • depends_on proposition 20.7 Terminal speed and the approach to it ¶
    • depends_on example 20.8 A raindrop ¶
  • depends_on proposition 9.11 Continuous dependence on the initial data ¶
  • depends_on proposition 9.142 The differential equation of the sine amplitude ¶
  • depends_on theorem A.74 Flow of a time-dependent vector field ¶ ↺
  • depends_on theorem 13.125 Existence, uniqueness and smoothness of the flow ¶ ↺
  • depends_on theorem 9.34 Poincaré–Bendixson; quoted ¶
    • depends_on theorem 32.30 Poincaré–Bendixson, restated from Part II ¶ ↺