theorem A.769 The Lorenz system

open in the book · appendices/A-long-proofs.tex:37447 · p. 3169

Rests on

depends_on definition 32.62 The Lorenz system ¶
- depends_on definition 32.7 Conservative and dissipative flows ¶
  - depends_on theorem 32.6 Evolution of phase volume ¶
    - depends_on definition 32.3 Dynamical system, phase space, flow ¶
      - depends_on definition 13.82 Vector field ¶
      - depends_on definition 9.1 Ordinary differential equation ¶
    - depends_on theorem 7.133 Gauss ¶
      - depends_on definition 7.127 Simple regions ¶
      - depends_on remark 7.128 What the derivations below take as given ¶
      - depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
      - proves proof ch:05-real-analysis@proof-79 ¶
    - proves proof ch:15-nonlinear-dynamics-chaos@proof-3 ¶
- depends_on theorem 32.6 Evolution of phase volume ¶ ↺
- proves proof ch:15-nonlinear-dynamics-chaos@prooflink-1 ¶
depends_on proposition A.766 Nondimensionalisation ¶
- depends_on definition 31.51 The other similarity groups ¶
  - depends_on phenomenon 31.49 Dynamical similarity ¶
    - depends_on theorem 31.37 The Navier–Stokes equations ¶
      - depends_on theorem 31.36 The Newtonian constitutive relation ¶
      - depends_on theorem 31.22 Euler's equations of motion ¶
      - proves proof ch:14-fluid-dynamics@proof-18 ¶
    - proves proof ch:14-fluid-dynamics@proof-24 ¶
  - depends_on theorem D.2 Buckingham's $\Pi$ theorem ¶
    - depends_on equation D.3 eq:E-kernel-condition ¶
    - proves proof app:E-dimensionless@proof-1 ¶
- depends_on proposition A.765 The roll equations ¶
  - depends_on definition A.763 Two-dimensional rolls ¶
    - depends_on equation 31.11 eq:fluid-incompressible ¶
    - depends_on proposition A.761 The Boussinesq equations ¶
      - depends_on definition A.760 The convecting layer ¶
      - depends_on phenomenon 31.78 Convective onset at a computed threshold ¶
      - depends_on theorem 31.37 The Navier–Stokes equations ¶ ↺
      - proves proof app:A-long-proofs@proof-443 ¶
  - depends_on proposition A.761 The Boussinesq equations ¶ ↺
  - proves proof app:A-long-proofs@proof-444 ¶
- proves proof app:A-long-proofs@proof-445 ¶
depends_on theorem A.767 Marginal stability of the conducting state ¶
- depends_on phenomenon 31.78 Convective onset at a computed threshold ¶ ↺
- depends_on proposition A.766 Nondimensionalisation ¶ ↺
- proves proof app:A-long-proofs@proof-446 ¶
proves proof app:A-long-proofs@proof-447 ¶

Supports

depends_on remark A.771 What was assumed, and where it fails ¶
depends_on remark A.770 What the three variables and three parameters are ¶

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
`depends_on`	→	The Lorenz system	declared	appendices/A-long-proofs.tex:37487
`depends_on`	→	Nondimensionalisation	declared	appendices/A-long-proofs.tex:37487
`depends_on`	→	Marginal stability of the conducting state	declared	appendices/A-long-proofs.tex:37487
`depends_on`	←	What was assumed, and where it fails	declared	appendices/A-long-proofs.tex:37718
`depends_on`	←	What the three variables and three parameters are	declared	appendices/A-long-proofs.tex:37683
`proves`	←	app:A-long-proofs@proof-447	declared	appendices/A-long-proofs.tex:37491