definition 32.41 The horseshoe map

open in the book · parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1075 · p. 1093

ground object -- no derivation owed

Rests on

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 13.48 Differentiable manifold ¶
    - depends_on definition 13.45 Differentiable map on a topological space ¶
      - depends_on definition 13.44 Atlas ¶
      - depends_on definition 13.43 Coordinate system ¶
    - depends_on definition 13.48 Differentiable manifold ¶ ↺
- depends_on definition 9.1 Ordinary differential equation ¶

Supports

depends_on theorem 32.42 The horseshoe is a full shift, quoted ¶
- 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:1080
`depends_on`	→	Dynamical system, phase space, flow	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1086
`depends_on`	←	The horseshoe is a full shift, quoted	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1097