proposition 32.49 The small-denominator obstruction
open in the book ·
parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1235
· p. 1095
Rests on
- depends_on equation 22.18 eq:ham-generating ¶
- depends_on equation 23.52 eq:hj-angle-linear ¶
- proves proof ch:15-nonlinear-dynamics-chaos@proof-17 ¶
Supports
-
depends_on
definition 32.50
Diophantine frequency vector
¶
-
depends_on
theorem 32.51
Kolmogorov–Arnold–Moser, quoted
¶
- depends_on phenomenon 32.58 Regular and chaotic motion coexist ¶
- depends_on phenomenon 32.59 The solar system is chaotic ¶
- depends_on remark 23.33 Integrability is exceptional ¶
-
depends_on
theorem 32.51
Kolmogorov–Arnold–Moser, quoted
¶
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:ham-generating | declared | parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1250 |
depends_on |
→ | eq:hj-angle-linear | declared | parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1250 |
depends_on |
← | Diophantine frequency vector | declared | parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1294 |
proves |
← | ch:15-nonlinear-dynamics-chaos@proof-17 | declared | parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1253 |