definition 32.8 Attractor and basin
open in the book ·
parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:212
· p. 1083
- 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 13.71
Differentiable curve
¶
-
depends_on
definition 13.81
Vector on a manifold
¶
- depends_on definition 9.1 Ordinary differential equation ¶
-
depends_on
definition 13.82
Vector field
¶
-
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
definition 6.1
Topological space
¶
- depends_on equation 3.51 eq:set-indexed ¶ ↺
-
depends_on
definition 6.2
Open set
¶
-
depends_on
definition 6.5
Open cover
¶
Supports
-
depends_on
definition 32.29
Limit cycle
¶
-
depends_on
phenomenon 32.35
Self-sustained oscillation
¶
-
depends_on
phenomenon 32.37
Frequency demultiplication and the first heard chaos
¶
-
depends_on
definition 32.91
The circle map
¶
- depends_on proposition 32.93 The circle map loses invertibility at $K=1$ ¶
-
depends_on
definition 32.91
The circle map
¶
-
depends_on
phenomenon 32.37
Frequency demultiplication and the first heard chaos
¶
-
depends_on
phenomenon 32.35
Self-sustained oscillation
¶
-
depends_on
definition 32.67
Strange attractor
¶
- depends_on example 32.70 The Hénon map ¶
- depends_on phenomenon 32.97 Turbulence sets in after a few transitions ¶
- depends_on phenomenon 32.68 Strange attractors ¶
-
depends_on
theorem 32.74
Oseledets, quoted
¶
-
depends_on
phenomenon 32.72
Sensitive dependence on initial conditions
¶
- depends_on definition 32.67 Strange attractor ¶ ↺
-
depends_on
phenomenon 32.72
Sensitive dependence on initial conditions
¶
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 |
→ | Dynamical system, phase space, flow | declared | parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:219 |
depends_on |
→ | Compact set | declared | parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:219 |
depends_on |
← | Limit cycle | declared | parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:677 |
depends_on |
← | Strange attractor | declared | parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2046 |
depends_on |
← | Oseledets, quoted | declared | parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2241 |