definition 32.62 The Lorenz system

open in the book · parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1856 · p. 1102

ground object -- no derivation owed

Rests on

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 13.81 Vector on a manifold ¶
    - depends_on definition 9.1 Ordinary differential equation ¶
  - depends_on theorem 7.133 Gauss ¶
    - depends_on definition 7.127 Simple regions ¶
      - depends_on definition 7.98 Functions of class $C^{1}$ ¶
      - depends_on definition 6.9 Compact set ¶
    - depends_on remark 7.128 What the derivations below take as given ¶
      - depends_on definition 7.125 Multiple integral ¶
      - depends_on theorem 7.40 Continuous functions are integrable ¶
      - depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
    - depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
      - depends_on definition 7.41 Antiderivative ¶
      - depends_on theorem 7.42 Fundamental theorem of calculus, I ¶
      - proves proof ch:05-real-analysis@proof-25 ¶
    - 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 ¶

Supports

depends_on theorem A.769 The Lorenz system ¶
- 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
`cites`	→	Deterministic Nonperiodic Flow	derived	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1882
`depends_on`	→	Conservative and dissipative flows	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1887
`depends_on`	→	Evolution of phase volume	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1887
`depends_on`	←	The Lorenz system	declared	appendices/A-long-proofs.tex:37487
`proves`	←	ch:15-nonlinear-dynamics-chaos@prooflink-1	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1890