example 32.80 The middle-thirds Cantor set

open in the book · parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2367 · p. 1108

example -- no derivation owed by its kind

Rests on

depends_on definition 32.79 Box-counting dimension, restated from Part II ¶
- depends_on definition 7.142 Box-counting dimension ¶
  - depends_on definition 7.140 Hausdorff measure ¶
    - depends_on axiom 7.1 Completeness of $\R$ ¶
    - depends_on definition 7.138 Set of measure zero ¶
      - depends_on definition 7.125 Multiple integral ¶
      - depends_on definition 3.65 Countable set ¶
    - depends_on definition 6.24 Metric ¶
      - depends_on definition 3.43 Map ¶
      - depends_on definition 3.38 Ordered pair and Cartesian product ¶
  - 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 6.5 Open cover ¶ ↺
depends_on theorem 32.42 The horseshoe is a full shift, quoted ¶
- depends_on definition 32.41 The horseshoe map ¶
  - 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 ¶ ↺

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type	direction	node	provenance	where
`depends_on`	→	Box-counting dimension, restated from Part II	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2381
`depends_on`	→	The horseshoe is a full shift, quoted	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2381