A rotationally-invariant form of this theorem developed by Gabriella Pinzari circumvents a nondegeneracy condition on the matrix of Birkhoff invariants that was mistakenly assumed in its original application. For 10 points each:
[10h] Name this theorem in nonlinear dynamics which states that for small perturbations, most frequencies define phase-space tori with quasiperiodic flows.
ANSWER: KAM theorem [or Kolmogorov–Arnold–Moser theorem; prompt on Arnold’s theorem]
[10e] Pinzari fixed Arnold’s application of the KAM theorem to the solar system, which was only correct in this case. Interest in this classic example of a chaotic system arose from studying the Earth–Moon–Sun system.
ANSWER: three-body problem [or three-body system; prompt on n-body problem]
[10m] To prove KAM using the Lie (“lee”) transform method, one starts by subtracting this operation of a generator and the unperturbed Hamiltonian. Canonical transformations preserve this operation, denoted by curly brackets.
ANSWER: Poisson bracket [prompt on PB]
<Jeremy Cummings, Physics>