phenomenon 32.97 Turbulence sets in after a few transitions

open in the book · parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:3045 · p. 1116

phenomenon-tested: no experiment declares a \tests edge to it and it is not listed in untested.txt

Rests on

depends_on definition 32.67 Strange attractor ¶
- depends_on definition 32.8 Attractor and basin ¶
  - depends_on definition 32.3 Dynamical system, phase space, flow ¶
    - depends_on definition 13.82 Vector field ¶
      - depends_on definition 13.81 Vector on a manifold ¶
    - depends_on definition 9.1 Ordinary differential equation ¶
  - depends_on definition 6.9 Compact set ¶
    - depends_on definition 6.5 Open cover ¶
      - depends_on definition 6.2 Open set ¶
      - depends_on equation 3.51 eq:set-indexed ¶
- depends_on phenomenon 32.72 Sensitive dependence on initial conditions ¶
  - depends_on equation 32.4 eq:chaos-linearization ¶
  - depends_on theorem 32.74 Oseledets, quoted ¶
    - depends_on definition 32.8 Attractor and basin ¶ ↺
    - depends_on definition 32.73 Lyapunov spectrum ¶
      - depends_on equation 32.45 eq:chaos-variational ¶
  - proves proof ch:15-nonlinear-dynamics-chaos@proof-25 ¶
depends_on remark 32.69 The Ruelle–Takens proposal and what displaced Landau ¶
proves proof ch:15-nonlinear-dynamics-chaos@proof-33 ¶

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type	direction	node	provenance	where
`cites`	→	Onset of Turbulence in a Rotating Fluid	derived	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:3051
`cites`	→	On the nature of turbulence	derived	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:3056
`cites`	→	Stability of a viscous liquid contained between two rotating cylinders	derived	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:3058
`depends_on`	→	Strange attractor	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:3059
`depends_on`	→	The Ruelle–Takens proposal and what displaced Landau	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:3059
`proves`	←	ch:15-nonlinear-dynamics-chaos@proof-33	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:3062