phenomenon 32.37 Frequency demultiplication and the first heard chaos

open in the book · parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:924 · p. 1091

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

Rests on

depends_on phenomenon 32.35 Self-sustained oscillation ¶
- depends_on definition 32.29 Limit cycle ¶
  - depends_on corollary 32.5 Trajectories do not cross ¶
    - depends_on proposition 32.4 The flow is a one-parameter group ¶
      - depends_on definition 32.3 Dynamical system, phase space, flow ¶
      - depends_on theorem 9.8 Picard–Lindelöf ¶
      - proves proof ch:15-nonlinear-dynamics-chaos@proof-1 ¶
    - depends_on theorem 9.8 Picard–Lindelöf ¶ ↺
    - proves proof ch:15-nonlinear-dynamics-chaos@proof-2 ¶
  - depends_on definition 32.8 Attractor and basin ¶
    - depends_on definition 32.3 Dynamical system, phase space, flow ¶ ↺
    - depends_on definition 6.9 Compact set ¶
      - depends_on definition 6.5 Open cover ¶
- depends_on equation 32.10 eq:chaos-vdp-si ¶
- proves proof ch:15-nonlinear-dynamics-chaos@proof-12 ¶
proves proof ch:15-nonlinear-dynamics-chaos@proof-13 ¶

Supports

depends_on definition 32.91 The circle map ¶
- depends_on proposition 32.93 The circle map loses invertibility at $K=1$ ¶

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`	→	Frequency Demultiplication	derived	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:933
`depends_on`	→	Self-sustained oscillation	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:936
`depends_on`	←	The circle map	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2806
`proves`	←	ch:15-nonlinear-dynamics-chaos@proof-13	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:939