definition 32.79 Box-counting dimension, restated from Part II

open in the book · parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2340 · p. 1108

ground object -- no derivation owed

Rests on

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 axiom 7.1 Completeness of $\R$ ¶ ↺
      - depends_on definition 7.39 Darboux sums and the definite integral ¶
    - depends_on definition 3.65 Countable set ¶
      - depends_on axiom 3.33 Peano axioms ¶
      - depends_on definition 3.62 Equipotence ¶
  - depends_on definition 6.24 Metric ¶
    - depends_on definition 3.43 Map ¶
      - depends_on definition 3.24 Quantifiers ¶
      - depends_on definition 3.28 Set ¶
    - 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 definition 6.1 Topological space ¶
    - depends_on equation 3.51 eq:set-indexed ¶
depends_on definition 6.5 Open cover ¶ ↺

Supports

depends_on definition 32.81 Correlation dimension ¶
depends_on example 32.80 The middle-thirds Cantor set ¶

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`	→	Box-counting dimension	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2364
`depends_on`	→	Open cover	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2364
`depends_on`	←	Correlation dimension	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2396
`depends_on`	←	The middle-thirds Cantor set	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2381