theorem 32.74 Oseledets, quoted

open in the book · parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2233 · p. 1106

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 definition 32.73 Lyapunov spectrum ¶
- depends_on equation 32.45 eq:chaos-variational ¶

depends_on phenomenon 32.72 Sensitive dependence on initial conditions ¶
- depends_on definition 32.67 Strange attractor ¶
  - 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 ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`cites`	→	A Multiplicative Ergodic Theorem. Lyapunov Characteristic Numbers for Dynamical Systems	derived	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2240
`depends_on`	→	Attractor and basin	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2241
`depends_on`	→	Lyapunov spectrum	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2241
`depends_on`	←	Sensitive dependence on initial conditions	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2177