phenomenon 32.72 Sensitive dependence on initial conditions

open in the book · parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2158 · p. 1105

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

Rests on

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 32.3 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 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 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 ¶

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`	→	Deterministic Nonperiodic Flow	derived	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2172
`cites`	→	A Multiplicative Ergodic Theorem. Lyapunov Characteristic Numbers for Dynamical Systems	derived	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2169
`cites`	→	Determining Lyapunov exponents from a time series	derived	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2175
`depends_on`	→	eq:chaos-linearization	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2177
`depends_on`	→	Oseledets, quoted	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2177
`depends_on`	←	Strange attractor	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2046
`proves`	←	ch:15-nonlinear-dynamics-chaos@proof-25	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2180