definition 32.67 Strange attractor

open in the book · parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2037 · p. 1104

ground object -- no derivation owed

Rests on

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 13.71 Differentiable curve ¶
      - depends_on definition 13.45 Differentiable map on a topological space ¶
      - depends_on definition 13.48 Differentiable 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 definition 6.1 Topological space ¶
    - 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 ¶

Supports

depends_on example 32.70 The Hénon map ¶
depends_on phenomenon 32.97 Turbulence sets in after a few transitions ¶
depends_on phenomenon 32.68 Strange attractors ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`cites`	→	On the nature of turbulence	derived	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2044
`depends_on`	→	Attractor and basin	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2046
`depends_on`	→	Sensitive dependence on initial conditions	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2046
`depends_on`	←	The Hénon map	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2133
`depends_on`	←	Turbulence sets in after a few transitions	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:3059
`depends_on`	←	Strange attractors	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2062