definition 32.73 Lyapunov spectrum
open in the book ·
parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2220
· p. 1106
- ground object -- no derivation owed
Rests on
- depends_on equation 32.45 eq:chaos-variational ¶
Supports
- depends_on proposition 32.86 The logistic map at $r=4$ is exactly solvable ¶
- depends_on proposition 32.76 The exponents sum to the mean divergence ¶
- depends_on proposition 32.77 A flow has a zero exponent ¶
-
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 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
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 |
→ | eq:chaos-variational | declared | parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2230 |
depends_on |
← | The logistic map at $r=4$ is exactly solvable | declared | parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2556 |
depends_on |
← | The exponents sum to the mean divergence | declared | parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2267 |
depends_on |
← | A flow has a zero exponent | declared | parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2297 |
depends_on |
← | Oseledets, quoted | declared | parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2241 |