theorem 32.42 The horseshoe is a full shift, quoted

open in the book · parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1089 · p. 1093

Rests on

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 13.71 Differentiable curve ¶
      - depends_on definition 13.45 Differentiable map on a topological space ¶
      - depends_on definition 13.48 Differentiable manifold ¶
  - depends_on definition 9.1 Ordinary differential equation ¶
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 definition 3.31 Empty set ¶
      - depends_on definition 3.35 Union, intersection, difference ¶
      - depends_on definition 3.30 Subset ¶
      - depends_on equation 3.51 eq:set-indexed ¶
  - depends_on equation 3.51 eq:set-indexed ¶ ↺

Supports

depends_on example 32.80 The middle-thirds Cantor set ¶
depends_on proposition 32.43 What the shift does ¶

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`	→	Differentiable dynamical systems	derived	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1096
`depends_on`	→	The horseshoe map	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1097
`depends_on`	→	Compact set	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1097
`depends_on`	←	The middle-thirds Cantor set	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2381
`depends_on`	←	What the shift does	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1106